This work aimed to evaluate the chemical composition and antibacterial activity of essential oils of Cymbopogon citratus (CCEO), Cymbopogon khasianus (CKEO), and Mentha arvensis (MAEO) against two Gram-negative (Escherichia coli, Klebsiella pneumoniae) and three Gram-positive (Staphylococcus aureus, Micrococcus luteus, Bacillus subtilis) microbial strains and their combination with antibiotics (chloramphenicol, ampicillin, erythromycin) to observe the synergistic behavior between them. The essential oils (EOs) were investigated by the GC-MS (gas chromatography mass spectrometry) method. The synergistic effect between EOs and antimicrobial agents was analyzed by broth dilution assay. (-)-carvone (52.48%), geraniol (57.66%), and citral (37.83%) were the major components identified in EOs of MAEO, CKEO, and CCEO, respectively. According to the antibacterial activity, EOs demonstrated strong antibacterial activity with MIC values ranging from 0.7 to 18 mg/mL. The interaction between the combination of EOs and antibiotics was determined in terms of FICI (Fractional Inhibitory Concentration Index). Some combinations displayed a partial synergistic effect, and some showed a synergistic and others displayed no effect against bacterial strains. The best synergistic action was shown by the combination of CCEO and Chloramphenicol against E. coli with a FICI value of 0.4. Three to four fold reductions in the MIC value of both essential oil and antibiotics were observed. Therefore, this synergistic interaction of the most active EOs with synthetic antibiotics could lead to new combination therapies for combating infections caused by multidrug-resistant microbes at sufficiently low concentrations in the pharmaceutical and food industry.