Unless your raised bed around the house is sitting on a slab of
concrete, the soil and mulch will settle over time, and by the time the
mulch "no longer functions as mulch", you'll probably have enough
settling that you'll be able to put new mulch right on top.

You are right to say that the mulch will settle. The mulch in my
garden probably has settled by half of the original thickness after
three years. I probably can put in one more inch of mulch over the
existing mulch without reducing the clearance around the house
foundation by too much.

Thanks for pointing this out.

You could also use a stone or gravel mulch right next to the house --
like the first 6-12" from the foundation, and start the organic mulch
away from the house.

I have thought of that. But I have a feeling that the organic mulch
will spill over to the inorganic mulch and I will have a hard time
cleaning the mix of organic mulch and inorganic mulch. This is one of
the reason why I don't like to use inorganic mulch.

Seem like no one suggests using weed killer. Oh well...

Jay Chan