By far the vast majority of those that tell you to "never, ever put mulches mext to your house" are people that have a vested insterst in selling you something to control termites. While termites may well move around in wood chip mulches, just as ants, millipedes, centipedes, pill bugs, etc. will thye are no more likely to invade your house then if you had no mulch down.
Perhaps this from Iowa State University might be of some help.

Here is a link that might be useful: Termites and mulch

Thanks a lot! Anyone ever have termites and used mulch anyway? Thanks again!

Hi & welcome to GardenWeb.

All I can say is I've never had termites, and always used mulch.

A groundcover plant would absolutely help as well. To be most effective it should grow thickly enough to block light from the soil. Without knowing where you are, specific plant suggestions are impossible but your local garden center should have some good candidates. I like Veronica, if that's a possibility for you. Just make sure it's something that will stay in the space where you want it. See what's available, then research before you spend your money. A layer of cardboard under your mulch would probably be beneficial to you at this point. There are probably a lot of weed seeds in the soil and a lot of them wouldn't be stopped by mulch. I would do the cardboard & mulch this year, then add groundcover(s) next year.