Misfire when the A/C is on?

Hello, the air conditioning has a pretty heavy load on the engine, and that is why you're feeling the misfire more when it's on. Has the check engine light come on or been on at any time?
Something to note about Hondas, especially with the higher mileage you have, is that the valves need to be adjusted as routine maintenance. Not many vehicles need valve adjustments anymore, but Hondas still do in most cases. And an intake or exhaust valve that is getting tight will show up more when there is a load on the engine such as the AC. But it should still be treated as a basic misfire when being diagnosed. Just to be sure it's not a failing ignition coil or fuel injector.
If you are comfortable with engine work, Ill post the instructions for adjusting the valves. With these you only need a set of feeler gauges, a 10mm wrench and a flathead screwdriver. After removing the valve cover, you turn the engine over by hand with a socket and bar on the crankshaft pulley bolt. So, you can line up each cylinder to the top dead center on the compression stroke, this way the camshaft is not pushing either of the valves open and can be adjusted. It needs to be done if the valves have never been adjusted. The valve cover gasket also needs to be replaced after the adjustment is done.

But here are some guides below to determine what is causing the misfire:

https://www.2carpros.com/articles/engine-misfires-or-runs-rough

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

https://www.2carpros.com/articles/how-to-test-an-ignition-system

https://www.2carpros.com/articles/how-to-test-engine-compression