Is a mezzanine lender's claim on the business paid before or after my bank loan?

After, in essentially every typical acquisition financing structure. Mezzanine financing is deliberately positioned between senior bank debt and the buyer's own equity in the overall capital structure, meaning it is structured, usually through an intercreditor or subordination agreement, to rank behind the senior bank lender's security in a default or insolvency scenario, in exchange for the mezzanine lender typically charging a higher return and sometimes taking an equity component to compensate for that added risk.

That said, the exact ranking in any specific deal is still ultimately a matter of what the financing documents actually say rather than an automatic legal default that applies regardless of drafting, so this should be confirmed against the actual subordination or intercreditor terms in a given transaction rather than assumed purely from how mezzanine financing typically works in the market. A buyer arranging layered financing involving both senior debt and mezzanine capital should make sure the priority arrangement between the two is clearly documented before closing, since ambiguity here can create real problems if the business later runs into financial difficulty.