Here's how it works if you invest any HSA money:
Let's say you have a balance of $10,000 and invested $5,000 in the market.
Mint will now list your account as:
HSA-whatever-bank $5,000 (cash)
Fidelity/whatever the brokerage is $5000 (investment)
The bank side of your account will always be listed as a cash account as any other bank savings / checking account would be. The part that is in the market will be listed separately in your investments category.
I'll also take this opportunity to say the banks are asshats because if it wasn't for their stupid minimum balance requirements/associated fees, I'd be investing all of my HSA money right now rather than a paltry 1/5 of it. So before you choose to invest, read the account documents. Odds are the parent bank requires a minimum balance of something ridiculous like $5000 to dodge a $5 "monthly account maintenance fee".