The baby beehinds bamboo fitteds are not all in one. They are one size fits all (OSFA) and need a waterproof cover. They don't need a liner. They come with snap in boosters but you need to buy the cover separately. You can use the cover more than once (I usually use them about 3 times each I think) before it needs to be washed. I like the BBH but they do take a bit longer and if your DF is so dead set on AIO then prob not your best option!
The only AIO I have is a BBH Magic All. I like it but I haven't bothered to buy or try any more cos I'm too cheap and am making do with what I have