First thought: coverture. Coverture is the legal idea that a married couple is one entity, with the wife not having an actual legal identity of her own. This is why there's the old-fashioned convention of women taking on their husband's entire name (e.g. "Mrs. Robert Smith"), why men could control any inheritance or money their wives had, and also the origin of some now-obsolete laws (like making it impossible for a wife to sue her husband for damages, because it's as if she was suing herself).
This is why it was so important for women to marry well: even if you worked as a married woman (and many women did), your money wasn't actually yours. It's one thing to have to live with a drunk asshole; it's worse to have that drunk asshole be the sole person who decides if that paycheck goes towards rent or more booze.
So, having a trinity/three parts of one whole entity would totally fit Victorian ideas of coverture. I think you'd still have it be men > everyone else, because they'd expect some kind of hierarchy, and even within the Trinity, God is still the leader.
Second thought: separate spheres. The Victorian era was very heavily focused on men being involved in the "dirty" business of work/politics/etc., and women being more morally pure and better suited to the domestic sphere (the whole "angel of the house" thing). Obviously this wasn't actually or practically true a lot of the time, but it was the aspired-to standard, the thing you'd measure people against to say if they were acting appropriately as members of their gender or not.
So you'd need a third sphere for Honorables to inhabit that is completely separate from the work/domestic dichotomy, or create an entirely different three-way dichotomy. Basically, you'd need a thing to point to, like "X is very ladylike" or "Y is not manly," but for Honorables.
You'd still have "Mr. and Mrs. Robert Smith," it'd just be, "Mr., Mrs., and Mx. Robert Smith" (differentiating by title, not by first name). I could actually see there being a different title for unmarried vs. married Honorables, like Master vs. Mister or Miss vs. Madam/Missus. Mix vs. Max, maybe?
I think Honorables would definitely need to have some kind of dowry. It actually might be even more necessary, because unless the guy is insanely wealthy on his own, you're going to need enough money to support three people, not just two.
I'm having trouble coming up with a third sphere, but whatever that third sphere was, you'd need to heavily police it. "You can't do X, that's for Honorables" has to be part of the culture. And you'd need to police it with as much weird pseudoscientific and/or religious justification as possible. Like, you need "women's brains physically can't handle the strain of learning math" but to explain why Honorables can't swim, or whatever.
