While the ebola virus infects a lot of human cells, immune system cells it infects are mainly monocytes and macrophages. The cells in our body mainly responsible for adaptive immunity, T cells, are at least not completely infected:
Our data indicate that 20–30% of CD4 and CD8 T cells died during the course of infection1
That's a lot, but the ones that survive get activated and it's apparantly enough that between 80 and 10% of the infected (depending on the strain) can survive the infection. Little is known about the details of the immune reaction to ebola, but the immune system does get activated. The immune system even remains on "high alert" for quite some time after infection and recovery.
And the antibodies do stick around, at least for 10 years. Whether they confer immunity against all strains of ebola, we don't seem to know - ebola isn't very well-researched yet.