AN ACR FLT CREW FLEW INTO A RESTRICTED AREA SHORTLY AFTER TAKEOFF WHILE FOLLOWING COMPANY PROCEDURES THAT LIMITED THEIR BANK ANGLE.

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WEATHER ON DEP WAS 1/4 SM AND 100 FT OVERCAST. WEATHER REMAINED SOLID IMC THROUGH AT LEAST 10000 FT. A NORMAL TKOF WAS PERFORMED OFF RWY 1. UPON PASSING 400 FT AGL WE STARTED A 1/2 BANK TURN (L TURN) TOWARDS A 300 DEG HDG. THIS EARLY TURN WAS MADE IN ACCORDANCE WITH AUTOMATED DATA PROCS. JUST PRIOR TO 1000 FT AGL THE CTLR TOLD US TO TURN FURTHER L TO INTERCEPT DCA 320 DEG R. AT 1000 FT LOW BANK WAS DESELECTED AND THE NOW FULL BANK TURN CONTINUED. A FEW MOMENTS LATER THE CTLR SAID 'TURN 15 DEGS L BEFORE YOU HIT THE OTHER ONE.' WE DID THAT AND INTERCEPTED THE DCA 328 DEG R. WE WERE HANDED OFF TO DEP WHO GAVE US A PHONE NUMBER TO CALL (DCA TRACON). WE NEVER INTENDED TO PENETRATE P56. I BELIEVE WE FOLLOWED COMPANY AND AUTOMATED DATA PROCS. (I DID NOT RECEIVE AUTOMATED DATA WITH THE RELEASE. I CONTACTED DISPATCH AND RECEIVED TKOF WEIGHTS AND DEP PROCS VERBALLY.) THE ALL ENGS OPERATING AUTOMATED DATA PROC OFF DCA RWY 1 STATES: 'ALL ENGS OEPRATING TURN ABOVE 400 FT AGL OK.' COMPANY PROC READS THAT ALL EARLY TURNS MUST BE PERFORMED AT '15 DEG LOW BANK MAX' UNTIL 1000 FT AGL AT A SPEED NOT LESS THAN V2. THIS PARTICULAR SECTION REFERS TO WEATHER OF 1000-3 OR BETTER. JUST ABOVE THAT SECTION IS THE REF THAT ALLOWS FOR EARLY TURNS WHEN REQUIRED BY 'SPECIAL DEP PROC.' AS WE WERE SOLID IMC; I READ THE COMBINED PROCS TO SAY TURN AT 400 FT AGL (AUTOMATED DATA PROC) AND THEN CLIMB IN 1/2 BANK TO 1000 FT AGL (COMPANY PROC) AND PASSING 1000 FT DESELECT 1/2 BANK AND CONTINUE WITH NORMAL PROCS. I THINK THE 1/2 BANK IS WHAT LED TO THIS EVENT. I FIND NO REF TO A PROC THAT SAYS WE CAN USE FULL BANK IN IMC ON THIS DEP (OR IN VMC FOR THAT MATTER). IF WE MUST USE FULL BANK TO AVOID P56 I WOULD LIKE TO SEE A PROC TO REFLECT THAT.