With the increasing prevalence of microbial infections, which results in prolonged inflammation and delayed wound healing, the development of effective and safe antimicrobial wound dressings of multiple properties remains challenging for public health. Despite their various formats, the available developed dressings with limited functions may not fulfill the diverse demands involved in the complex wound healing process. In this study, multifunctional sandwich-structured electrospinning nanofiber membranes (ENMs) were fabricated. According to the structural composition, the obtained ENMs included a hydrophilic inner layer loaded with curcumin and gentamicin sulfate, an antibacterial middle layer consisting of bovine serum albumin stabilized silver oxide nanoparticles, and a hydrophobic outer layer. The prepared sandwich-structured ENMs (SNM) exhibited good biocompatibility and killing efficacy on Escherichia coli, Staphylococcus aureus, and Methicillin-resistant S. aureus (MRSA). In particular, transcriptomic analysis revealed that SNM inactivated MRSA by inhibiting its carbohydrate and energy metabolism and reduced the bacterial resistance by downregulating mecA. In the animal experiment, SNM showed improved wound healing efficiency by reducing the bacterial load and inflammation. Moreover, 16S rDNA sequencing results indicated that SNM treatment may accelerate wound healing without observed influence on the normal skin flora. Therefore, the constructed sandwich-structured ENMs exhibited promising potential as dressings to deal with the infected wound management.