I pity you
As background info, in case you don't happen to know, the last version of FrontPage was in 2003, and the product was discontinued by MS in 2006. So you can't get support from MS on the product (I suspect, but I don't actually know that), which is typically a big deal for large companies.
But yes, I do feel it would not be correct of you to continue to develop code in other ways, when they've told you their position. They're writing the paychecks, not you. But I would make it very clear to them that there is significant liability in this limitation, whether it's out-dated or potentially non-supported software (are you using the FP Server Extensions too?), lack of support for changing internet technologies (throw html5 at them...), lack of support for mobile devices (no media queries), etc.
I would think convincing them at least to migrate to Expression Web might be possible.