Your phone sounds distinctive ring patterns, depending on which number was called. Normal modems don't care about distinctive ring, and will answer either pattern. Some modems, however, can be configured to answer only certain ring patterns. In addition, the distinctive ring service requires no special installation. There are alternatives to modems.
Most alternatives involve dedicated lines between home and office, which is expensive.
In addition, ISDN is much less sensitive to line noise, and can provide other benefits, depending on your configuration. ISDN is expensive for both equipment and the monthly service charge compared to standard phone lines. Still, the cost of ISDN is moving down, so this should become a popular alternative over the next couple of years. Most modems are attached to a computer. However, there are alternatives for offices with networks.