Sorry for your loss. 
In my experience cats and dogs have the exact same kind of afterlife as humans, insofar as it is complex: some will pass right on through seeking their next incarnations, some will move onto different and higher spiritual planes, some will remain in spirit form for a while.
They also have the same “architecture” of the soul as humans, when approached using basic core shamanic journeying: an incarnated self (your normal pet), and a Higher Self that has knowledge and power, for example.
I mentioned making a link with the HS of your pets in this post: Dogs and energies - #4 by Lady_Eva.
I am as certain pets have an afterlife as I am certain of anything, physical or spiritual, in this world. 
And I don’t have time to tutor people in the core shamanism method right now but if a group of people on this topic want to learn it together to contact pet’s Higher Selves (alive or passed on) shout me up and i’ll set up a group PM with the tutorials where you can swap notes?
I know exactly what you mean, again making contact with their HS may help, and often pets seem to get some kind of boost to their own ascent by helping us, so not all will come back - but some want to, I had this experience with a pet a while ago. 