An air carrier aircraft departed DCA and in an attempt to avoid heavy rain and turbulence turned slowly to the 328 radial; they entered P56 as a result.

Narrative

I was the First Officer and pilot flying. Takeoff was briefed and set up per airline's procedures (both pilots on raw data). Additionally; the DCA328 radial was entered on the legs page; thus depicting a magenta line on the navigation display. After takeoff I made an initial 30 degree bank left turn; visual with the Potomac River. We armed the VOR track so the FMS would capture the 328 radial. After entering IMC conditions around 1000 FT MSL the weather radar depicted moderate to heavy rain in our flight path and we were experiencing moderate turbulence. While attempting to avoid the heavier rain shafts I realized that I shallowed my bank angle while proceeding to intercept the DCA328 radial. We later reported the weather to Potomac Departure. Later in the flight we received a message we had broken the western boundary of P56. No mention of adverse weather was mentioned by the DCA tower. It would have been very useful to have had the information. Our radar did not show any red until we had started the turn towards the 328 radial. Weather was a critical factor in this occurrence. The lack of communication regarding weather on the departure path; from ATC; specifically the DCA Tower; contributed to our altering the prescribed flight path.