Yes, in this instance, it's okay to combine these herbs (chronic tonic and houttuynia), because there is nothing in there that would counter another herb. Not all herbs can be mixed though, so before doing so on your own, please do check with an experienced herbalist, or do a lot of research to be sure that it will be safe. Some herbs will potentiate other herbal actions (make them stronger) and other herbs will reduce the effectiveness of other herbal actions. So we must understand what we are doing, as herbs can be quite effective medicine!
Straining herbal powders from the tea is really messy, and that's why most don't do it - and just opt to drink it, "herbal soup" at the bottom and all. A fine weave coffee filter (paper) would catch most of the herbal soup though. And no, herbal powder does not dissolve in even the hottest of water - and that only dispels the essential oils of the plant, so typically, you need to cover the steeping pot.
If it's being made with herbs that are only cut and not powdered - often called "cut & sifted" - then you won't be drinking the sludge at the bottom, but you will need to strain it. This is how I made all of my teas - don't like drinking that "herbal soup"!!!
And just to clarify, they are both considered a decoction and an infusion when using all the herbs in the chronic tonic. That's because one refers to the aerial parts of the plant and one refers to using the stems and woody parts of the plant:
"Infusions are used with the softer parts of plants and require a long soak to coax vitamins, minerals, and more out of the herbs into the water. An herbal decoction is employed when extracting constituents from hard or woody plant parts such as roots, bark, seeds, berries, and mushrooms."/theherbalacademy.com/herbal-decoction/
Best of luck to you and your husband, WesternBrit!!!