An air carrier pilot reported that Company policy required one pilot to display Terrain while the other pilot displayed Weather. If weather is present but terrain is flat; both pilots should be in weather for proper avoidance and discussion.

Narrative

A dark and stormy night. Autopilot engaged. Captain flying RNAV departure...electing to use Terrain display because I had selected weather. I could see thunderstorms in departure path - not rain - clear cut line of cells -and had to draw his attention to it because he was not displaying weather. At one point we nicked the edge of a cell; along with some real big bumps. We were way to close to the Big Red Blobs. In maneuvering to clear the weather; the Captain neglected to call for slat retraction. Since I was nervous about the 'weather avoidance' strategy and was closely monitoring the flight path. I did not complete the climb checklist; I became absorbed in the weather situation; and I did not notice slat extended. At 280 KTS 'slat overspeed' sounded. One day later I checked the maintenance record to see what the corrective action was needed and I could find no record of the slat overspeed logged in the maintenance computer; even though the Captain wrote it up. Looks like it just disappeared. Recommendation - If there is weather in the departure area both pilots should be required to display; brief; and avoid the weather. Having Terrain displayed is of no value over flat areas; and Terrain will 'pop up' if a conflict is detected anyway. We should both be looking at the real threat in any given situation; and these 50;000 FT Texas thunderstorms can be a real threat.