I work compressed hours - 10 days over 9. For the last 2 years I've had every other Friday off and it's worked nicely - I'm quite introverted and I love just having a day to myself, cleaning, pottering about, reading, whatever. It's just me and DH, no children.
However about 6 months ago DH started a new job with more flexibility, and guess what...like most other people who have the option, he chooses to WFH on a Friday when he can (which is most of the time as he rarely needs to be in the office, the rest of his week is quite meeting-heavy). I worked out earlier I've not had one of my days off just by myself in over 3 months.
There isn't really anywhere he can be in the house that doesn't impact me - I can hear him working wherever I am (constant calls, loud voice), and I can't just hoover whenever/wherever I like, or have the radio up loud . Even if I try and sit and watch TV it's not relaxing as I have to turn it up loud so as not to hear him. I do occasionally ask him to go into the office instead which he does, but I then get messages asking if he can come home early, have I finished having my 'quiet time' etc. He basically wants to be here on a Friday because it's his one opportunity in the week to WFH, which tbf I can understand (I WFH full time for context). He will try and keep his voice down, and he will try and keep out of my way, but it's just not the same.
So I think my only option is to ask to change my day, maybe to a Wednesday or something. But it doesn't have the same appeal as a Friday for some reason! If you have a mid-week day, does it work well for you?