So to establish one fact: The human vagina is designed for human sex- which involves protecting the uterus from the outside world (no cervical penetration, which you already don't think happens), and keeping the semen by the cervix for as long as possible while gravity (and the eventual thinning of human semen) does it's work. It's why the cervix "dips" into the vagina- that extra space allows semen to pool and take longer to leave.
That out of the way, the sperm cells themselves (not the fluid that makes up the majority of any mammal semen) do enter the OS of the cervix. This is much more difficult outside of ovulation, where the cervical mucus is very thick- though it still happens (thanks to cervical folds that restrict and protect the sperm, this is why a woman can get pregnant outside of ovulation). During ovulation, the mucus becomes thinner and allows more sperm to pass more easily.
Now it's important to note that all sperm is treated as a foreign invader by the woman's body, including human sperm. It's also important to note that the uterus will help move all sperm cells up into it. At this point, a woman's body doesn't discriminate against sperm species. The sperm moves forward, the uterus helps point it and up it goes.
This process goes all the way to the egg itself, if present, where the actual species discrimination occurs. The Zona Pellucida has receptors on it that prevent cross-species fertilization. While Humans and Canine have homologus genes for some of these protein receptors, they don't completely match. Canine sperm may try to move towards the egg to inseminate it, but won't be able to. They also won't block human sperm from inseminating the egg, as by this time so few sperm are there- and the egg is so big in size comparison- that there's plenty of room for human sperm to do it's work.
It's actually fascinating that (at least mammals) have evolved a system to keep their eggs from being fertilized by the wrong species of sperm. Almost like interspecies sex has been so common in nature that evolution had to account for it.
While it's possible for an improperly formed Zona Pellucida to allow a canine sperm to inseminate (and effectively kill) the egg, this would involve a genetic abnormality that tends towards infertility in women. In these cases, the woman has to have a doctor perform the fertilization in a lab to get pregnant, as these issues also cause problems with human sperm fertilizing the egg (too many fertilize the egg, sperm won't implant, etc.).
Incidentally, they used to test human sperm for fertility by removing the Zona Pellucida on hamster eggs, then observe how well the sperm fertilized them. This wasn't a very good test, they found out, so it's been largely phased out for better methods.
TLDR: At the microscopic level, your dog does inseminate you the same as a human man would, but the egg completely ignores the dog sperm knocking at it's door.
