It depends. This is a complex issue you've asked, and a one or two sentence answer won't explain or be of much help, so bear with me.
Species within the same genus are capable of hybridization, but will not do so unless forced into it. If you maintain several of each species, you are more likely to have male and female, and they will spawn within their species.
The genus Corydoras is unique because it is a polyphyletic genus. This means the species currently assigned to this genus have not descended from the same ancestor. All species that have descended from the same ancestor are termed a lineage, or sometimes a clade. There are in fact nine distinct lineages in the present genus. So with the above in mind, only species within the same lineage would be able to hybridize. But again, keeping several of each species is not likely to result in cross-spawning.
Turning to the lineages for the species you mention, the pepper cory is probably the species Corydoras paleatus. This species is in lineage 6.
Now we have another issue, namely, is your "julii" really C. julii? Most cories sold as "julii" are actually C. trilineatus. In order to fully answer your question, I'll consider both species. As it turns out, both C. julii and C. trilineatus are in lineage 9. That means they (whichever) will not hybridize with C. paleatus.
