I really think the level of comfort or discomfort varies according to the mindset of the individual person, the relationship between the two partners, and the way cross-dressing is first introduced into the relationship. My spouse is mtf transgender, but about two years before he (we aren't using feminine pronouns quite yet) realized he wanted to become a woman, he began to experiment with cross-dressing.
In our situation, my spouse, J, told me he was interested in cross-dressing from the start, and I really appreciated his openness about it, because that made me feel like I could trust him not to keep important things hidden from me. I personally have no issues with cross-dressing as a concept. Women can 'cross-dress' whenever they want to in today's society, and I don't see why men shouldn't have that same freedom. All the same, it did take me a week or so to get used to the idea. As cliche as it may sound, one of my first reactions was to ask J if he was still attracted to me. That was my biggest concern, and when he reassured me that he was, I felt a lot better. Since then, J and I have shopped together, done our makeup together, and I've done his hair. Really, speaking as a girl who never got into the whole hair and makeup thing as a teen, I've been improving my own skills in this arena. And we've had fun.
My advice to you isn't too different from what everybody else here has said. Talk to your S.O. and find out what her biggest concerns are about your cross-dressing. If she's feeling insecure, reassure her. If she doesn't want you to wear her clothes, ask her why. My spouse and I raid each other's clothes, but that isn't something every couple will be comfortable with. Also, see if you can make things fun. A girl's night in is a great idea, if she is open to it.