Could somebody explain me the difference between その上 and 上に?. In "A dictionary of intermediate japanese grammar" it is written that they can be used interchangeably, but I am not sure if it meant that they are always interchangeable or that there are cases where they can be used indifferently.
その上 is a conjunction that means "in addition (to that)", so it is used like 私は英語が得意、その上、絵も上手.
A noun 上 has many meanings and 上に is "a noun 上 + a particle に". https://dictionary.goo.ne.jp/jn/17464/meaning/m0u/ So there are many usages of it.
You can say 私は英語が得意な上に、絵も上手. This meaning is the same as 私は英語が得意、その上、絵も上手.