A Captain reported encountering strong turbulence at FL280 accompanied by a 500 FT altitude gain with a nose down attitude. Because static blocked communications with ATC and the flight was off altitude; the crew squawked 7600 then 7700. There were no injuries.

Narrative

After holding for arrival over SPS we decided to divert. Between SPS and our divert airport there was significant weather observed to our east and west. We were IMC as we were proceeding south. The weather we could see was displayed on the radar but nothing was painting ahead of us (our 12 o'clock). As we began to encounter light to moderate chop I instructed the Flight Attendants to take their seats. Approximately 5 minutes later; we hit turbulence strong enough to cause the autopilot to disengage. I attempted a few resets but it continued to disengage. Simultaneously to this event; due to static; we lost communication with Center. At one point; while manually flying; I had some degrees nose down and was climbing at more than 500 FT per minute. I think our maximum deviation was 400 FT higher than assigned. Since we had no communication and unable to hold altitude; I instructed First Officer to squawk 7600 and 7700 respectively. After several minutes of this turbulence and icing we broke out of the weather and proceeded to our destination without further incident. Because of our inability to 'maintain complete control of the aircraft; ie; altitude' and the nature of the turbulence I entered in the event in maintenance. Fortunately; there were no injuries.