I'm having the same problem right now with my guitar...

There are several possibilities:
1 - The strings are too old. After as little as 4 or 5 weeks, strings can go out of tune (unless they're coated strings, like Elixir). The B and high E strings are the ones that go out first.
2 - You're pressing the B string too hard when playing the D chord. This would cause it to go sharp, leaving it flat when you play the E chord.
3 - The neck is off (I have no knowledge about how that problems happens or how to fix it).
4 - The bridge is off. Take it into a guitar store that will take your guitar apart and tell you what the problem is. They'll fix the bridge if necessary.