This girl wants to come over my house, but I live in a townhouse and she lives in a pretty big single family house. Nothing is more embarrassing than being poorer than your girl.
I lived in the projects growing up. You have nothing to lose by inviting her over. If she doesn’t think you are good enough for her based on where you live, she is not good enough for you.
Don’t worry about it. There are lots of good reasons to live in a townhouse. Ease of maintenance and convenience to things like jobs and shopping and relatives are some examples of reasons.
I think townhouses are beautiful homes! If she has respect toward you, she will have respect toward your home! 
There are a whole lot of things more embarrassing. One of them is being ashamed of your family. This would be a big red flag for a good girl.
We’ve always lived in townhouses, some nice, some more modest. My kids were friends with kids who lived in gated communities, with live in help and multi-car garages. They weren’t embarrassed.
Nothing is more embarrassing than being poorer than your girl? Someday you may have a wife. How are you going to handle it if she earns more than you? I hope neither of you would have an attitude about it. Just invite your friend over. If she has an attitude, she’s not good enough for you.
Oh man, I know how you feel. Where I live, people live in HUGE houses, drive Mercedes, BMWs, and even Porsches and Bentleys. I’m nowhere near their level of affluence, but my best friends are wealthy, and they don’t treat me any different. She should respect you, and not think of you any different because of where you live, and if she does, she’s not good for you. It’s not easy not being able to give your girlfriend everything you want, but hopefully they understand your situation and know how much you care, I know mine does. Don’t worry, and don’t not invite her over because you’re worried, she could be ‘the one!’ Hope this helped!
Please do not worry! If your girl is a great person, she will respect you not based on wealth but you as a person! I know I’m repeating things other people said before, but I wanted to emphasize that. You matter, and we’re all here to help you. I know it can be embarrassing to go through what you are, but there is no need to. She really could be “the one”, like @tvpeople said. Go for it!
Have a good day!
A well-kept, tidy townhouse can be much more pleasant to visit than a moldy, dirty single-family home. It’s all about how clean your place is, in my opinion.
I agree with @yucca10 and @austinmshauri and would like to add that the girl’s family may be rich, but I’d be willing to bet that she hasn’t earned any of those riches herself, so you’re on an equal playing field, as far as I’m concerned. Unless one of you has a job and the other is a couch bum; that might be embarrassing…
I can’t imagine it will be the slightest issue (and if it is she probably isn’t a friend you will want to keep). . As you go though life you will find that there are always people who have more than you do and people who have less than you.
I’ve been embarrassed by my home. It’s a modest single family home but it is filled with old, broken hand-me-downs.
What has been really nice is finding friends who feel comfortable sitting on my ripped sofa, with me being comfortable with them sitting there.
There is nothing like having a friend with that level of comfort.
I hope you find friends like that.
FWIW, I don’t feel completely comfortable in houses unless they are a little messy, especially upscale houses.