Two adults, three kids. Arriving at the airport and needing to get to Interlaken. Train is looking like it would cost a fortune.

Any ideas on what the cheapest option might be?

Could be wrong but I think the key to decent priced public transport in Switzerland is getting travel passes (some of which are regional), that give you big discounts on fares. That’s about as far as my knowledge goes though! Could you do one way hire on a car?

Do they still do that Swiss Transfer Ticket thing? (Never used them myself, but I thought it was a fixed price to get basically anywhere by train from any incoming flight)
edit: yes, but it’s many more CHF than I thought.

Most Swiss pay for a railcard which gives them a 50% discount. That however will not be cost effective for you.

I would suggest you contact the tourist office and/or your hotel in Interlaken and ask if there are any deals/packages being offered on the train. Alternatively the tourist office may know of companies running transfers.