Suggestions

[miloyip]

1. using namespace std in header file will pollute all implementation files that include the header. The practice is to use std::string, std::vector, etc. in header.
2. Use size_t instead of int for size of array/object and indices. Otherwise there are a lot of related warnings.
3. Currently, these APIs returns jValue by value.

jValue operator[](int i);
jValue operator[](string s);

This will make a deep copy of the whole subtree for every call.
If the library is designed for read-only access to the parse result (as I cannot find APIs for modifying existing values), I will suggest to change all APIs as const member functions:

string to_string() const;
jType get_type() const;
int as_int() const;
double as_double() const;
bool as_bool() const;
string as_string() const;
size_t size() const;
const jValue& operator[](size_t i) const ;
const jValue& operator[](const string& s) const;

While the other write-access API can be private and makes parser friend of jValue.