Multi-energy　microgrids　(MEMG)　play　an　important　role　in　promoting　carbon　neutrality　and　achieving　sustainable　development.　This　study　investigates　an　effective　energy　management　strategy　(EMS)　for　MEMG.　First,　an　energy　management　system　model　that　allows　for　intra-microgrid　energy　conversion　is　developed,　and　the　corresponding　Markov　decision　process　(MDP)　problem　is　formulated.　Subsequently,　an　improved　double　deep　Q　network　(iDDQN)　algorithm　is　proposed　to　enhance　the　exploration　ability　by　modifying　the　calculation　of　the　Q　value,　and　a　prioritized　experience　replay　(PER)　is　introduced　into　the　iDDQN　to　improve　the　training　speed　and　effectiveness.　Finally,　taking　advantage　of　the　federated　learning　(FL)　and　iDDQN　algorithms,　a　federated　iDDQN　is　proposed　to　design　an　MEMG　energy　management　strategy　to　enable　each　microgrid　to　share　its　experiences　in　the　form　of　local　neural　network　(NN)　parameters　with　the　federation　layer,　thus　ensuring　the　privacy　and　security　of　data.　The　simulation　results　validate　the　superior　performance　of　the　proposed　energy　management　strategy　in　minimizing　the　economic　costs　of　the　MEMG　while　reducing　CO2　emissions　and　protecting　data　privacy.