When I was a teenager in the 70s the labels we used for two people who were romantically involved but did not live together and had not bound themselves legally in marriage were...
I can see an argument that the terms Girlfriend and Boyfriend might not be specific enough. In other words, someone might want to separate such a relationship based either on chastity or some common-law legal precedent that I'm unaware of.1 But I don't know of one that's universally accepted with one possible exception: "significant other."
I also recognize the growing trend of gender ambiguation that leads to a desire to not use terms that establish gender. The unfortunate truth is we're 50-100 years away from commonly used terms recognizable outside the subculture. I am not trying to marginalize, exclude or in any other way suggest that there shouldn't be terms that better describe these kinds of situations. But today, 99% of the U.S. population would barely understand such terms when used (e.g., "living together apart," which I experienced for the first time in this post) and wouldn't use them out of habit.
Please note that part of the problem is that there is no definition for what makes a "living together apart" relationship true or false other than the claim of the partners. Excluding a marriage committment, what defines a committed relationship? Sexual intimacy? No. Spending time together? No. Paying each other's medical bills? Maybe. Combining incomes? Probably. Is the condition temporary? ("My partner is working in Dubai for three years, so we're living together apart because we use the same checking account") or permanent? ("My partner lives a couple of miles away. We share the same bank account, but pay for different residences...") That ambiguity is why terms like Girlfriend and Boyfriend continue to be used and why you're having so much trouble locating a term to replace those words.
Today in the U.S., if you describe a couple such as you have and label them using Girlfriend and/or Boyfriend you would not be misunderstood.
BTW, In my area using the word "cohabitants" would get you the same funny stares as using the term "coitus" for "sexual intimacy." Here, it's considered a technical term. The term we would use for people living together unmarried in a sexual relationship is "partners." I wouldn't be surprised if the term changed with region.
1 In some U.S. states, if you live together in a committed relationship long enough, you are considered married for the purpose of legal ownership of property. This is called "common-law marriage" and in some instances the government would refer to the members as "spouses." However, this is a legal distinction and its use by the public would surprise me. I expect that whatever term is used by the couple to identify their relationship is what their neighbors would use.