Usually the rule is that you need 10 or more high card points and a 5+ card suit to respond at the 2 level. A 2H bid would be forcing 1 round on opener, but if opener raises responder's suit, rebids his own suit at the cheapest level, or bids NT at the cheapest level, then responder may pass with a minimum.
examples of sequences where responder is not forced to bid again:
On your example hand, even though I only have 9 HCP, I think it would be best to stretch to bid 2
♥ because of the fitting diamond honors, and the nice honor structure in hearts. If you changed the heart ace to the Q, then I would make a negative double. If you changed the club 3 to the club ace, then it would be a clear 2
♥ call.