Mulch against wood is generally not a good thing (think trees and the caveat to keep mulch away from the trunk) but how much it will speed decay will vary. How thick of a mulch were you planning to use and could it be kept thin near the beds? How's the drainage in the paths (keeping the mulch wet)? If the wood is in contact with the ground, it will wick water up unless there is a "sacraficial" furring strip on the bottom. You coud do something similar on the sides if it appears the mulch will stay damp for long periods.

tj

I have 2 x Cedar lumber as frames around trees with wood chip mulch inside and have not found that the mulch contributes that much to rot. The 2 x SPF lumber I used to frame my planitng beds did, even though sorrounded by grass, rot after 8 to 10 years. More then anything else it will depend on the type of wood you use then on whether mulch is used.
I found grass much easier to maintain around the planting beds then a mulched surface.

Wood will rot. It's just a matter of how long you can make it last but there's no permanent wood.