PHP is written in C
No, it isn't. It is written in EnglishIt is written in English.
There are multiple implementations, only one of which (Zend Engine) is written in C. Quercus and P8 are written in Java, Phalanger and PeachPie are written in C♯, HippyVM is written in RPython (using the PyPy framework), HHVM is written in C++.
A language has semantics, syntax, and a type system. PHP has all of those.
Why is PHP not a library of C or jQuery a language in its own right?
jQuery has no semantics of its own, its semantics are the ones of ECMAScript, it has no syntax of its own, its syntax is the one of ECMAScript, it has no type system of its own, its type system is the one of ECMAScript.