<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q


                QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934


                        For Quarter Ended MARCH 31, 1998

                         COMMISSION FILE NUMBER 33-46573
                                                --------


                             CAPITAL HOLDINGS, INC.
                             ----------------------
             (Exact name of registrant as specified in its Charter)



         OHIO                                            34-1588902
         ----                                            ----------
(State or other jurisdiction of             (I.R.S. Employer Identification No.)
incorporation or organization)



                     5520 MONROE STREET, SYLVANIA, OH 43560
                     --------------------------------------
              (Address of principal executive offices and zip code)


                                 (419) 885-7379
                                 --------------
              (Registrant's telephone number, including area code)


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15 (d) of the Securities Exchange Act of 1934
during the preceding 12 months (or for such shorter period that the registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.
                  (1) YES    X        (2) NO
                         ---------          ---------

As of March 31, 1998, there were 2,000,510 shares of common stock outstanding.


<PAGE>   2


                             CAPITAL HOLDINGS, INC.

                                      INDEX




<TABLE>
<CAPTION>
                                                                                            PAGE NUMBER
                                                                                            -----------
<S>                                                                                              <C>
PART I.  FINANCIAL INFORMATION
------------------------------


Item 1.           Financial Statements (Unaudited):

                  Consolidated balance sheets
                           March 31, 1998 and December 31, 1997                                  3

                  Consolidated statements of income
                           Three months ended March 31, 1998 and 1997                            4

                  Consolidated statements of shareholders' equity
                           Three months ended March 31, 1998 and 1997                            5

                  Consolidated statements of cash flows
                           Three months ended March 31, 1998 and 1997                            6

                  Notes to consolidated financial statements                                     7


Item 2.           Management's Discussion and Analysis of Financial Condition
                  and Results of Operations                                                      8 - 9




PART II.  OTHER INFORMATION                                                                      10
---------------------------


SIGNATURES                                                                                       11
----------
</TABLE>



                                                                              2


<PAGE>   3




                             CAPITAL HOLDINGS, INC.
                           CONSOLIDATED BALANCE SHEETS



<TABLE>
<CAPTION>
                                                                         (UNAUDITED)
                                                                        MARCH 31. 1998    DECEMBER 31. 1997
                                                                        --------------    -----------------
<S>                                                                       <C>                  <C>         
ASSETS
    Cash and due from banks                                               $ 15,293,896         $ 15,291,951
    Federal Funds Sold                                                            --              8,000,000
                                                                          ------------         ------------
    Total Cash and Cash Equivalents                                         15,293,896           23,291,951

    Investment Securities Available for sale, at fair value                177,947,131          167,520,873

    Loans                                                                  481,085,040          469,036,091
         Less: Allowance for credit losses                                   7,140,895            6,947,377
                                                                          ------------         ------------
    Net loans                                                              473,944,145          462,088,714

    Bank premises and equipment                                              9,524,068            9,548,218
    Interest receivable and other assets                                     8,333,679            7,090,107
                                                                          ------------         ------------
Total Assets                                                              $685,042,919         $669,539,863
                                                                          ============         ============

LIABILITIES AND SHAREHOLDERS' EQUITY
    Deposits:
         Interest bearing                                                 $545,556,594         $544,186,632
         Noninterest bearing                                                52,051,862           49,869,745
                                                                          ------------         ------------
    Total deposits                                                         597,608,456          594,056,377

    Short-term borrowings                                                   27,900,000           15,900,000
    Interest payable and other liabilities                                   7,545,194            9,036,804
                                                                          ------------         ------------
Total Liabilities                                                          633,053,650          618,993,181

SHAREHOLDERS' EQUITY
    Common stock, no par value, $.50 stated value;
         3,000,000 shares authorized and 2,000,510 shares
         issued and outstanding (1,991,922 at December 31, 1997)             1,000,255              995,961
    Capital in excess of stated value                                       33,448,875           33,179,413
    Retained earnings                                                       16,406,821           15,014,646
    Unrealized net holding gains on securities available for sale            1,133,318            1,356,662
                                                                          ------------         ------------
Total Shareholders' Equity                                                  51,989,269           50,546,682
                                                                          ------------         ------------
Total Liabilities and Shareholders' Equity                                $685,042,919         $669,539,863
                                                                          ============         ============
</TABLE>



See Accompanying Notes

                                                                               3



<PAGE>   4



                             CAPITAL HOLDINGS, INC.
                  CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED)

<TABLE>
<CAPTION>
                                                                     THREE MONTHS ENDED
                                                                           MARCH 31
                                                                  1998                1997 
                                                              -----------         -----------
<S>                                                           <C>                 <C>        
Interest income:
       Loans, including fees                                  $10,204,402         $ 8,476,832
       Securities                                               2,690,627           2,586,010
       Federal funds sold                                         114,572              47,465
                                                              -----------         -----------
Total interest income                                          13,009,601          11,110,307

Interest expense:
       Deposits                                                 6,962,076           5,909,806
       Short-term borrowings                                      480,057             362,714
                                                              -----------         -----------
Total interest expense                                          7,442,133           6,272,520
                                                              -----------         -----------
Net interest income                                             5,567,468           4,837,787

Provision for credit losses                                       230,000             240,000
                                                              -----------         -----------
Net interest income after provision for credit losses           5,337,468           4,597,787

Other income:
       Securities gains, net                                       13,210               3,750
       Other                                                      330,740             264,362
                                                              -----------         -----------
Total other income                                                343,950             268,112

Other expenses:
       Salaries and employee benefits                           1,604,423           1,334,575
       Equipment                                                  193,642             110,269
       Taxes other than income                                    120,475             106,173
       Courier services                                           143,253             127,286
       Net occupancy                                               71,269              74,728
       Other                                                      856,074             749,151
                                                              -----------         -----------
Total other expenses                                            2,989,136           2,502,182

                                                              -----------         -----------
Income before provision for federal income tax                  2,692,282           2,363,717

Provision for federal income tax                                  880,000             770,000
                                                              -----------         -----------

Net income                                                    $ 1,812,282         $ 1,593,717
                                                              ===========         ===========

Net income per share:
   Basic                                                      $      0.91         $      0.84
                                                              ===========         ===========
   Diluted                                                    $      0.90         $      0.81
                                                              ===========         ===========

Average shares outstanding:
   Basic                                                        1,998,444           1,898,118
                                                              ===========         ===========
   Diluted                                                      2,023,934           1,974,781
                                                              ===========         ===========
</TABLE>


See Accompanying Notes



                                                                               4






<PAGE>   5



                             CAPITAL HOLDINGS, INC.
          CONSOLIDATED STATEMENTS OF SHAREHOLDERS' EQUITY (UNAUDITED)
                   THREE MONTHS ENDED MARCH 31, 1998 AND 1997



<TABLE>
<CAPTION>
                                                                                 COMMON STOCK                       CAPITAL IN
                                                                    --------------------------------------           EXCESS OF
                                                                          SHARES               AMOUNT              STATED VALUE 
                                                                    -----------------    -----------------    --------------------

<S>                                                                        <C>                   <C>                 <C>          
Balance at January 1, 1998                                                 1,991,922             $995,961            $33,179,413  

Net income                                                                                                                        

Unrealized gains (losses) on securities, net of tax                                                                              
                                                                                                                                 
Comprehensive Income                                                                                                              

Exercise of 4,250 common stock options at $16.44 per share                     4,250                2,125                 67,745  
                                                                                                                                 
Issuance of 4,338 shares of common stock at $47.00 per share                   4,338                2,169                201,717  

Cash dividend declared, $.21 per share
                                                                    --------------------------------------------------------------
Balance at March 31, 1998                                                  2,000,510           $1,000,255            $33,448,875  
                                                                    ==============================================================




Balance at January 1, 1997                                                 1,897,508             $948,754            $30,893,093  

Net income                                                                                                                        

Unrealized gains (losses) on securities, net of tax                                                                               
                                                                                                                                
Comprehensive Income                                                                                                              

Exercise of 1,022 common stock options at $10.78 per share                     1,022                  511                 10,506
                                                                                                                                
Issuance of 312 shares of common stock at $37.50 per share                       312                  156                 11,544

                                                                    --------------------------------------------------------------
Balance at March 31, 1997                                                  1,898,842             $949,421            $30,915,143  
                                                                    ==============================================================





<CAPTION>
                                                                                                OTHER               TOTAL
                                                                         RETAINED           COMPREHENSIVE        SHAREHOLDERS'
                                                                         EARNINGS              INCOME               EQUITY
                                                                    -----------------------------------------------------------

<S>                                                                       <C>                  <C>                 <C>        
Balance at January 1, 1998                                                $15,014,646          $1,356,662          $50,546,682

Net income                                                                  1,812,282                                1,812,282

Unrealized gains (losses) on securities, net of tax                                              (223,344)            (223,344)

                                                                                                               ----------------
Comprehensive Income                                                                                                 1,588,938

Exercise of 4,250 common stock options at $16.44 per share                                                              69,870 

Issuance of 4338 shares of common stock at $47.00 per share                                                            203,886 

Cash dividend declared, $.21 per share                                       (420,107)                                (420,107)
                                                                    -----------------------------------------------------------
Balance at March 31, 1998                                                 $16,406,821          $1,133,318          $51,989,269
                                                                    ===========================================================




Balance at January 1, 1997                                                 $9,217,448            $530,809          $41,590,104

Net income                                                                  1,593,717                                1,593,717

Unrealized gains (losses) on securities, net of tax                                            (1,323,318)          (1,323,318)

                                                                                                               ----------------
Comprehensive Income                                                                                                   270,399

Exercise of 1,022 common stock options at $10.78 per share                                                              11,017

Issuance of 312 shares of common stock at $37.50 per share                                                              11,700

                                                                    -----------------------------------------------------------
Balance at March 31, 1997                                                 $10,811,165           ($792,509)         $41,883,220
                                                                    ===========================================================
</TABLE>






See Accompanying Notes
                                                                               5



<PAGE>   6


                             CAPITAL HOLDINGS, INC.
                CONSOLIDATED STATEMENTS OF CASH FLOWS (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                          THREE MONTHS ENDED
                                                                                               MARCH 31
                                                                                        1998              1997
                                                                                   ------------       ------------
<S>                                                                                <C>                <C>
OPERATING ACTIVITIES:
    Net Income                                                                     $  1,812,282       $  1,593,717
    Adjustments to reconcile net income to net
       cash provided by operating activities:
            Provision for credit losses                                                 230,000            240,000
            Depreciation and amortization                                               161,146             78,086
            Amortization and accretion of security premiums and discounts                (3,576)           (38,283)
            Gain on sale of securities                                                  (13,210)            (3,750)
            Deferred income taxes                                                       (78,200)           (81,600)
            Changes in assets and liabilities:
                Increase in interest receivable and other assets                     (1,050,317)          (944,321)
                (Decrease)/increase in interest payable and other liabilities        (1,573,285)           717,135
                                                                                   ------------       ------------
    Total adjustments                                                                (2,327,442)           (32,733)
                                                                                   ------------       ------------
    Net cash provided by operating activities                                          (515,160)         1,560,984

INVESTING ACTIVITIES:
    Purchase of securities available for sale                                       (18,615,440)       (14,044,592)
    Net increase in loans                                                           (12,085,431)       (27,712,207)
    Purchase of bank premises and equipment                                            (136,997)        (2,141,464)
    Proceeds from maturities of securities available for sale                           854,257          4,504,339
    Proceeds from sales of securities available for sale                              7,013,313          1,003,750
                                                                                   ------------       ------------
    Net cash used in investing activities                                           (22,970,298)       (38,390,174)

FINANCING ACTIVITIES:
    Net increase in deposits                                                          3,552,079         65,131,652
    Net increase/(decrease) in short-term borrowings                                 12,000,000        (25,222,545)
    Issuance of common stock                                                            273,756             22,717
    Dividends paid                                                                     (338,432)              --
                                                                                   ------------       ------------
    Net cash provided by financing activities                                        15,487,403         39,931,824
                                                                                   ------------       ------------

Increase in cash and cash equivalents                                                (7,998,055)         3,102,634
Cash and cash equivalents at beginning of period                                     23,291,951         13,958,201
                                                                                   ------------       ------------
Cash and cash equivalents at end of period                                         $ 15,293,896       $ 17,060,835
                                                                                   ============       ============

Supplemental disclosures:
    Interest paid                                                                  $  7,527,276       $  6,083,172
                                                                                   ============       ============
    Income taxes paid                                                              $    175,000       $    100,000
                                                                                   ============       ============
</TABLE>

See Accompanying Notes



                                                                               6



<PAGE>   7


                             CAPITAL HOLDINGS, INC.


                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                    FOR THE THREE MONTHS ENDED MARCH 31, 1998

                                   (UNAUDITED)




BASIS OF PRESENTATION
---------------------

The unaudited consolidated financial statements include the accounts of Capital
Holdings, Inc. (the Company) and its wholly owned subsidiaries, Capital Bank,
N.A. (the Bank) and CBNA Building Company, which is a real estate subsidiary
that owns and leases to the Bank, its only operating facility.

The accompanying unaudited consolidated financial statements have been prepared
in accordance with generally accepted accounting principles for interim
financial information and with the instructions of Form 10-Q and Article 10 of
Regulation S-X. Accordingly, they do not include all of the information and
footnotes required by generally accepted accounting principles for complete
financial statements. All adjustments (consisting of normal recurring accruals)
considered necessary for a fair presentation have been included. Significant
intercompany balances and transactions have been eliminated in the consolidated
financial statements. For further information refer to the consolidated
financial statements and notes thereto appearing in the Company's annual report
on Form 10-K for the year ended December 31, 1997.

The Bank's maximum exposure to credit losses for loan commitments and standby
letters of credit outstanding at March 31, 1998 was $211,339,000 and
$12,573,000, respectively, compared to $186,909,000 and $13,439,000,
respectively, at December 31, 1997. The increase in loan commitments is due to
owner-occupied real estate construction to take place within the next twelve
months. Management does not anticipate any significant losses as a result of
these commitments.


COMPREHENSIVE INCOME
--------------------

As of January 1, 1998, the Company adopted Statement 130, Reporting
Comprehensive Income. Statement 130 establishes new rules for the reporting and 
display of comprehensive income and its components; however, the adoption of
this Statement had no impact on the Company's net income or shareholders'
equity. Statement 130 requires unrealized gains or losses on the Company's
available-for-sale securities, which prior to adoption were reported separately
in shareholders' equity, to be included in other comprehensive income. Prior
year financial statements have been reclassified to conform to the requirements
of Statement 130.




                                                                               7



<PAGE>   8


                             CAPITAL HOLDINGS, INC.


           MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                            AND RESULTS OF OPERATIONS




The Company's primary asset is its subsidiary bank, which is in its ninth year
of operation. For the three months ended March 31, 1998, the Bank experienced an
increase in net deposits. Deposits increased $3,552,000 or .6% during the first
quarter of 1998.

Loan growth for the first quarter of 1998 was $12,049,000 or 2.6%. The allowance
for credit losses at March 31, 1998, was $7,141,000 or 1.5% of total loans,
compared to $6,947,000 or 1.5% of total loans at December 31, 1997. The Bank had
write offs totaling $36,000 during the first quarter of 1998. Nonperforming
loans represent .05% of total loans at March 31, 1998. Management considers the
allowance to be adequate at this time. At March 31, 1998, the Bank had no
impaired loans.

Securities available for sale totaled $177,947,000 or 26.0% of total assets at
March 31, 1998. The Bank continues to maintain very high investment quality with
81.2% of total securities in U.S. Treasury and Agency securities. The Bank has
no high-risk on or off balance-sheet derivatives. The total market value of the
portfolio decreased $223,000 (net of tax) during the first quarter of 1998. This
is a reflection of the fluctuation in bond rates on both long and short-term
security maturities. The Bank's portfolio has a weighted average life to
maturity of approximately 2.2 years.

Consolidated net income for the first quarter of 1998 was $1,812,200 or $.90 per
share. This compares to $1,594,000 or $.81 per share for the first quarter of
1997. The increase in income before provision for federal income taxes,
excluding securities gains, for the three months ended March 31, 1998,
represents a 13.2% increase over the same period of 1997. This increase is a
direct result of growth in earning assets, careful attention to noninterest
expenses and an increase in fees collected on lending transactions. The income
tax provision of approximately 33% for the three months ended March 31, 1998,
remained comparable to the same period last year.






                                                                               8



<PAGE>   9


                             CAPITAL HOLDINGS, INC.

           MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                            AND RESULTS OF OPERATIONS


Other expenses continue to increase as the Bank grows. Net overhead as a
percentage of average assets has remained the same at 1.77% for the year ended
December 31, 1997, and for the three months ended March 31, 1998. Salaries and
benefits represent 53.7% of other expenses for the three months ended March 31,
1998. Salary expense for the three months ended March 31, 1998, increased 20.2%
over the same period for 1997. Staff levels have increased from 86 to 103 (full
time equivalents) over the past 12 months, to accommodate the increase in growth
of the bank. Average assets per employee has increased from $6,203,000 at
December 31, 1997, to $6,553,000 at March 31, 1998.

The Tier I Capital ratio was 9.89%, the Total Capital ratio was 11.14%, and the
Leverage ratio was 7.53% at March 31, 1998, compared to regulatory capital
requirements of 4%, 8% and 4%, respectively. These ratios are well in excess of
the regulatory capital requirements.

Shareholders equity has continued to increase from retained earnings of net
income. A $.21 per share cash dividend was declared on March 31, 1998, payable
on April 25, 1998. Annualized, this cash dividend represents 22% of the current
years projected earnings.

In June 1997, the Financial Accounting Standards Board (FASB) issued Statement
of Financial Accounting Standards (SFAS) No. 131, Disclosures about     
Segments of an Enterprise and Related Information.  The Company expects that
adoption of this Statement will not have a significant impact on the
consolidated financial statements.






                                                                               9


<PAGE>   10


                             CAPITAL HOLDINGS, INC.




PART II.  OTHER INFORMATION
---------------------------



ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

    (a) Exhibits

        27    Financial Data Schedule


    (b) No reports on Form 8-K were filed for the quarter ended March 31, 1998.









                                                                              10




<PAGE>   11


                                   SIGNATURES


Pursuant to the requirements for the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.





                                         CAPITAL HOLDINGS, INC.





Date     5/8/98                            /s/ Michael P. Killian
    ------------------              ---------------------------------------

                                    Michael P. Killian, Chief Financial Officer,
                                               Senior Vice President









                                                                              11