There was a time when there was no digital. For those of us who started on film, there was never a choice, and the question did not exist. Some, however, would bring a back-up camera in case their main one had issues.
In this regard, you are dealing with proven technology. So long as your camera is in good repair, there is not much to worry about.
I suppose it depends on how confident or experienced you are with film. If you are taking snapshots, and have a good point-and-shoot or range-finder, there should not be any problems. If you have an SLR and are good with it, still, not much to worry about.
Many family trips were documented with cheap and basic 35mm or 120 cameras with no real settings, and things generally came out fine. We have stacks of old vacation and family photos taken with 126 cameras, and I recently revived one of those cameras and am confident in it.
You can consider your digital as the "backup." Even shoot with it regularly, but decide the film camera is your primary camera for the trip. That way you are safe with what you are confident in (digital), but are concentrating on film.
Also, you could try a sort of systematic desensitization. Use only film for things nearby before going on a trip. This may help you become more confident with film before using it on an important trek. Perhaps even make mistakes on purpose (on test rolls); this will give you an idea of what you can get away with. You may be surprized how robust film photography is.
If you are worried about lack of instant feedback, try taking digital pictures, but not looking at the LCD after the shot - wait until you get home before you look. Get used to trusting yourself to get the picture - don't let the computer think for you. Think of it as touch-typing. When you get good at it, you know what you have.
I do not own a digital camera, and have no qualms using film for anything I am doing. I just take snapshots, and my composition sucks, but I know I will get a picture of what I want. The only serious problems I've ever had were user error, which I could do just as easily with digital.
One word of advice whether you do all film or both... make sure you bring enough film. My best friend and I went to New England about 4 years ago, and I thought I was well stocked... I was not. I nearly bought out a local drugstore; they had a lot of Kodak 200 because it was a tourist area, but it was at tourist drugstore prices. My best friend had a digital camera, and she had to be paranoid about backing it up every night. I just put my exposed film in a cooler.
Today we went to the baptism of my best friend's sister's adopted daughter. They handed me an Olympus Stylus and asked me to take pictures (I told them had I known, I'd have brought a pro 120 camera). Anyway, the flash took forever to recharge, and the camera took too long to save each picture. I missed a few shots simply waiting for the camera to ready itself (I did some test shots w/o flash, and they were unacceptable in the sharpness department). Add the fact the camera's battery doesn't like to be at the ready (because I wasn't going to let it turn off as I didn't want to miss a shot), we had to change batteries mid-ceremony. My 35mm would have run circles around it (including a reload), and my 1980s consumer-grade flash recharges faster. (I'm sure an expensive DSLR would have been just as fast, but most people don't have super-fast high-end digital equipment.)