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Can you? Yes. Is it advisable? Probably not.
Being a restaurant owner, interior designer, and working in the navy seems nearly impossible, provided that you want to do any of them well. You would be pulled in too many directions to be very effective at any of them. That said, you might be able to do two, but with great effort. Managing a restaurant is an extremely difficult and time consuming activity, with large numbers of staff to juggle, opening and closing hours that are quite long, and fickle customers. Owning a restaurant may mean you are managing it, but it might also mean that you're the primary investor in a business that someone else is managing. The time obligations will be very different.
I want to address a possible underlying issue. You can do anything you want, but the challenge is to do something really well. If you love interior design, you could spend the better part of a career working to achieve mastery of that field. The same goes for work in the restaurant industry. Your family might be worrying that if you spread your attention too thin, you won't be able to achieve the mastery that is required for you to be very successful in your fields of choice.
There's good news too: if you decide not to work on two new fields at once, you could always build them up. If you think interior design is a strength, then build up an interior design business over a couple of years. Once it gets stable, and you're able to spend less time tending to the business, then open up your restaurant. It's not a foolproof way to achieve your dreams, but it's much more manageable. Most importantly, you'll have time to get really good and what you do. Good luck!