An error made in an effort to avoid error is more socially damaging than street talk. If you have ever said "between you and I," "him and I," or "her and I" (patterns which are grammatically incorrect under all circumstances), you need this lesson. Errors are ridiculous in direct proportion to the effort expended in making them.
When faced with the formula "X and Y," where either word is a pronoun, choose each pronoun's form as if the "and" and the other word were not there. The reason that this works is that a sentence like
Sandy and her husband couldn't get a mortgage
is a combination of two separate propositions:
Sandy couldn't get a mortgage.
Her husband couldn't get a mortgage.
When you replace the nouns with pronouns in each proposition, you get
She couldn't get a mortgage.
He couldn't get a mortgage.
==>Sandy and he couldn't get a mortgage.
==>She and her husband couldn't get a mortgage.
On the other hand, combine two propositions like this:
The committee recommended him.
The committee recommended me.
==>The committee recommended him and me.