Are home values decreasing in your area? How much home equity do you currently have? Unless it is a very high number, you may be in danger of having your HELOC frozen by your bank, which means you could be unable to borrow any more money at 3.99%. Many banks have been doing this recently.
If you were in the $0 in savings and $11k balance scenario and needed $1,000 to fix the car or more for some other emergency, what would you do without the HELOC? I am guessing that this is the situation that might worry your spouse, it would worry me!