Having dealt with a lot of clients during my freelance career I can say that prefacing demos goes a long way. If your co-founder isn't part of the technical team then schedule demo times for input but preface those demos with the fact that they are rough'd in, or that you're just testing a new feature, or that the UI is just temporary.
People can always have good ideas; whether they're technical or not. The key is to find the right time to have those ideas introduced. A useful tool is to have a weekly show and tell; just like back in elementary school. Have your technical team sit down and hear what your business dev. and marketing teams are up to and vice versa.
To ultimately answer your question of: "how do you let them know you're making good progress even if the "UI" is not polished." Your other co-founder is either a.) very inexperienced, or b.) is very unreasonable. If you're finding a hard time talking about a simple demo to this person then look out for when bigger decisions and discussion come into play.