Antimicrobial resistance has been estimated to be responsible for over 700,000 deaths per year, therefore new antimicrobial therapies are urgently needed. One way to increase the efficiency of antibiotics is to use them in combination with bacteria-specific parasitic viruses, phages, which have been shown to exert additive or synergistic effects in controlling bacteria. However, it is still unclear to what extent these combinatory effects are limited by rapid evolution of resistance, especially when the pathogen grows as biofilm on surfaces typical for many persistent and chronic infections. To study this, we used a microcosm system, where genetically isogenic populations of Pseudomonas aeruginosa PAO1 bacterial pathogen were exposed to a phage 14/1, gentamycin or a combination of them both in a spatially structured environment. We found that even though antibiotic and phage-antibiotic treatments were equally effective at controlling bacteria in the beginning of the experiment, combination treatment rapidly lost its efficacy in both planktonic and biofilm populations. Mechanistically, this was due to rapid resistance evolution: while both antibiotic and phage selected for increased resistance on their own, phage selection correlated positively with increase in antibiotic resistance, while biofilm growth, which provided generalised resistance mechanism, was favoured most in in the combination treatment. Only relatively small cost of resistance and weak evidence for coevolutionary dynamics were observed. Together these results suggest that spatial heterogeneity can promote rapid evolution of generalised resistance mechanisms without corresponding increase in phage infectivity, which could potentially limit the effectiveness of phage-antibiotic treatments in the evolutionary timescale.