I would generally recommend avoiding the topic of your marital status.
Some employers may feel they can work their single employees into the ground with long hours; others realize working smarter not longer matters... a lot. Meaning, it can cut both ways. See:
https://www.washingtonpost.com/news/inspired-life/wp/2015/04/02/dont-be-a-bachelor-why-married-men-work-harder-and-smarter-and-make-more-money/If you stretched to bring it up, it would raise red flags for me that you don't know the unwritten rules of interviewing (which is those topics are to be avoided).
Having said that, if something comes up naturally, that's fine. I don't do outbound phone interviews, but I am on the interview team when someone interviewing for my organization comes in for their on-site day. When I interview in person my first question is "Tell me something I should know about you that isn't on your resume". That stumps some people (yellow flag - no life outside work?). Many have stellar answers. I've learned people do marquetry and some other really cool factoids about passions people have outside work. One (we hired him - now a colleague at work) responded with "I work for my family... blah, blah". Clear, concise, well founded reasoning. How he answered that question was critical. The content was irrelevant, albeit mentioning his family. Now having worked with him for a while, great guy, great work, and it's unquestionably his perspective on the world.
As far as the reliability part, find a story at work that demonstrates reliability. Have you been in a position where management gave you 8 days of work on two high profile projects to do in 3 days? Did you clearly communicate the intractable nature of the problem as soon as you knew? See if a question comes up where you can tell that story about the communication and how both projects were successful. This demonstrates (a) you took on what you could and fulfilled that commitment [a form of reliability] (b) communicated early when something was amiss [allowing the work to be sent to someone else so your manager could appear reliable to their boss] (c) Have the best interests of the company in mind and can think beyond the next day. This seems small, but I'm consistently amazed by the number of people I work with who just ignore requests because they are busy.
Other advice? Have questions ready for them, and those questions should be based on who you are talking to. HR types, ask about culture, why the job was posted, what surprises new hires to the company. If it's the manager, ask direct things about the job and how to be successful - tools, how employee measurement works, what is the top thing to do in the first 30 days, etc.