Yeah, the advice I got (and promptly ignored, to my great detriment) was always to feign interest in a PhD program when applying to grad school. My response was to your actually considering *getting* both.

A dual PhD might make more sense--or specifically looking at programs with a specialty in the kind of linguistics you're interested in. I mean, it looks like you're definitely in for a ling PhD regardless of what comes before, so it's mostly your compsci coursework and the amount of that you tie in to your diss that's going to matter, more than what degree(s) you have in computer science.

But yes, tell 'em you want a PhD if you want any support at all!