I suppose that depends on whether or not he tried to hide it from me, and to what extent it affects our relationship. If he never lied about it or deliberately tried to deceive me and it didn't change how he felt about me, then no problem. If he did try to deceive me, for whatever reason, then we could have a trust and honesty issue. If he's saying it because he's finding himself more attracted to another person than to me (male or female), then we'd have a much bigger problem.
To answer the other bit...yes, I think bisexuals can have every bit as good of a relationship as heterosexuals or homosexuals. One's orientation matters much less than their commitment to their chosen partner.