I'm a female monkey born 1968; he is a tiger born 1974. Is there hope in this relationship??

I am afraid that it may not be a good pair. Both of you square accounts in every detail and self-centered. You seldom concerns the other and the family. If you can learn to take care about the other and pay more attention on your family, you may have a happy marriage.
However, in my opinion, if you two love each other and can handle all the troubles through discussing, you can have a good marriage.