The brand of freewheel doesn't matter.
I have little experience with freewheels but am not aware of any which come 1/8." Most, if not all are 3/32" and I'd be surprised if the White Industries was not. .
1/8" chain will work with either 1/8" or 3/32" components, both fixed gear cogs and freewheels.
Solution: get a 1/8' chain or exchange the 1/8" fixed gear cog for a 3/32" cog and run your current chain. .
-Tim-