Bid 3H just like you did. This is forcing in "standard" (not that I have ever read this in a book on "standard" but I have never heard of any strong players using 3H here as a signoff - which is apparently how your partner read it).
It should be noted that if 1NT is weak (clearly it wasn't here) and if the responder is a passed hand (as he was here), it makes a lot more sense for 3H to be non-forcing.
Here is a nice (non-standard!) convention that you can use in this situation. I mentioned this the other day as a vugraph commentator and the audience (and other commentators) seemed to like this idea (as they should!).
When partner opens 1NT and they overcall 3D:
3H=invitational or better with 5+ spades
3S=forcing to game with 5+ hearts
When partner opens 1NT and they overcall 3C you can do even better:
3D=invitational or better with 5+ hearts
3H=invitational or better with 5+ spades
3S=forcing to game with 5+ diamonds
This is one of those rare conventions in which the advantages so clearly outweigh the disadvantages that I am not even going to bother explaining why this is the case
But this is not the sort of convention you want to use except in a serious partnership - too easy to forget it otherwise.
Fred Gitelman
Bridge Base Inc.
www.bridgebase.com