However, every time I mention that we should look into purchasing a house, he gets frustrated with me and tells me he is too busy with work right now, and/or he tells me that we first need to stop eating out so much.
Perhaps you just need to sit down at dinner (at home) one night and just ask him if he is even interested in buying a home at all. Are the two of you used to just traveling or going out with friends all the time - perhaps he does not want the responsibility of upkeep. I am a single woman and I bought my house (an older one) when I was 24. I have a large lot and there is the upkeep. I do what I can and what I can't I hire done, but I do know this - at this point in my life I do not want an apartment or even a condo. I have wonderful neighbors but they are not right on top of me and I can have lots of family and friends over for dinner and parties and fun in the yard.