I would go with the 2nd option (checkboxes) because:
Radio buttons usually express mutually exclusive options (EITHER this OR that), so giving an option that includes but excludes at the same time won't be consistent.
The checkboxes are used to select several items (this AND that) which is the case. Also take into account that it might happen that you have to add a new option and if you use radio buttons, you will have to redesign this control (remember users hate changes unless they're great improvements).
"Both" label has more cognitive load since it doesn't express something by itself, since it's a reference to another items. A way to improve it would be to explicitly named the label "Customer + Item", but the only case I would use it would be in the classic multiple choice exams, where you can find options like "Answer D: All previous answers are correct"