The level of protein structure that involves interactions between the side chains of the amino acids rather than interactions between molecules within the backbone is:

The tertiary protein structure

Explanation:

The primary protein structure consists of amino acids linked by peptide bonds to form a polypeptide chain. The secondary protein structure consists of hydrogen bonding to form an alpha helix / beta pleated sheet between carboxyl and amino groups of the polypeptide chain. Interactions between the side chain of amino acids are present in the tertiary structure where proteins started folding into it unique conformation.