Date: 201407
Local time of day: 0601-1200
Location: SDF.Airport, KY
Flight conditions: IMC
Light: Daylight
Aircraft: EMB ERJ 145 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
ATC / advisory: TRACON SDF; Tower SDF
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Confusion
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Inflight Event / Encounter Weather / Turbulence
Detector: Automation Aircraft TA; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: We were cleared for takeoff on Runway 17L at SDF 'amend altitude to maintain 3;000; RNAV to DROPA (STREP TWO RNAV) cleared for takeoff.'  After takeoff Tower advised us to turn left to 150 and contact Departure.  Departure gave us climb and maintain 10;000 and turn RIGHT to a heading of 060. I knew this was the long way around but we were surrounded by storms in all quadrants except south.  I assumed this turn was due to weather.  We were climbing at a steep angle to get above the weather and halfway through the turn Departure called us and told us to maintain 3;000 feet.  We were already passing 3;200 feet and told her unable.  She then called us and said descend immediately to 3;000 and gave us a heading but the heading part cut out. At the same time our TCAS was going off with 'TRAFFIC'.  First Officer immediately pushed the nose over to stop climb and descend back to 3;000.  I asked ATC what heading and she remained silent for a few seconds and then gave us; 'Immediate turn to 160;' which First Officer complied instantly.  TCAS did not give us an RA because one plane was about 1;000 feet above and the other was closing at 500 feet below.  All three aircraft converged at the same time and I think we flew right through the middle.  I advised ATC we have 2 planes and one below us and she replied; 'YEP.'  ATC had told us of the traffic when she said immediate descent to 3;000.  After the conflict she gave us another climb and turn and she asked us; 'Did I give you a left turn to 060 or a right turn to 060?' I said right turn to 060 and then she gave us another frequency. I think ATC gave us the wrong direction of turn i.e. RIGHT instead of LEFT.  By the time she caught the mistake it was almost too late.  TCAS couldn't help much because of the two airplanes in close proximity. I do remember repeating back to ATC RIGHT TURN TO 060; my First Officer heard the same thing.


Second narrative: [Report narrative contained no additonal information]


Synopsis: Air carrier flight crew describes an airborne conflict after takeoff from SDF when the Departure Controller issues a right turn to 060 while intending to issue a left turn. The clearance was not questioned due to the weather and the flight passed between two other aircraft; one 500 feet below and one 1000 feet above; without receiving a TCAS RA.