First, let's clear up the name: Edward Bulmer's Invisible Green is a mid-depth foliage green (LRV 28.6) — a soft, leafy colour with a warm yellow undertone, gently earthed by natural mineral pigments. It's not the very dark, near-black estate green you might be picturing; Little Greene's colour of the same name is that one. Bulmer's version is a green you can actually see, sitting comfortably in the middle of the wall.
That warmth is your steer for everything around it. On ceilings and trim, go for a soft off-white rather than a stark brilliant white. Paper III from Paint & Paper Library (LRV 75.3) is quiet and gently stony; Au Lait from Farrow & Ball (LRV 80) is milkier and a touch brighter. Either frames the green cleanly without the hard blue edge that makes a leafy colour look dusty.
For grounding, Cigar BH.20 from Mylands (LRV 11.8) is a smoky mid-depth tobacco brown — a natural partner for foliage green, branch against leaf. On a study door, joinery or a snug feature wall it makes the green read fresher by contrast.
Want a livelier note? Fuchsia Falls 2 from Dulux (LRV 29.8) is a bright, cool magenta-pink — close to green's true opposite — so a little of it goes a long way: cushions, a lampshade, the inside of a cupboard. Proper flower-against-leaf stuff. It's a punctuation mark, not a second wall colour.
Timber and brass both belong here. Old oak and unlacquered brass pick up the yellow buried in the green and make the whole room feel settled.
The "but what about" question: *can I drench it?* You can — at LRV 28.6 it's deep enough to feel enveloping in a snug with walls and woodwork together, without ever going cave-dark. In a bright room it stays garden-fresh all day.
Practical tip: sample it properly — two coats on a big board you can move around — and check it morning and evening. That yellow undertone comes up golden in afternoon sun and settles to a quieter olive in north light.