I would discourage learning C++ with C. C++ is not C with wings. It is a language, at the surface, that differentiates itself from C although, under the hood, much of C++ is backed by C. The problem of learning both at the same time is the danger of mixing the two languages together. I notice it is quite common for programmers new to C++ to do this and the net is rife with code that does this.
C++ on the surface is object-oriented and, as such, should be programmed at that level when learning so as to avoid many pitfalls where C code could cause unintended errors. I learned this lesson right here on this forum as was advised not to mix C++ and C. Other than that, it is fine to learn them both at the same time as many constructs in C will reappear in C++ but remember, they are two separate languages.