Is This Normal?

I just found out that my husband wears my lingerie around the house when I am at work. He wears heels, stockings, thongs, and skirts. I guess he used to do this prior to us dating and then stopped. He recently started again. He tells me he is not gay and that he wants to be with me. He just wishes he could stop wearing them, but he likes the way they feel. He said he just wants to be "normal". What do I do and say? Is this normal? Is it even possible he's not gay?

— Natalie, 28

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