Carrier-phase ambiguity resolution (AR) facilitates rapid and precise GNSS positioning. This work describes an integrity monitoring algorithm to ensure high integrity of AR-enabled GNSS positioning systems, such as PPP-RTK and RTK. Prior studies either (a) only focused on protecting ambiguity-float GNSS positioning against faulted observations (i.e., raw measurements or correction products) or (b) evaluated the integrity risk from incorrect ambiguity resolution while assuming the observations as fault-free. These approaches or their simple combinations cannot address the cases where observation faults threaten ambiguity-fixed GNSS positioning, because the occurrence of observation faults affects the risk from incorrect-fix events. The proposed approach can accommodate observation faults and incorrect-fix events simultaneously, through a modified multiple hypothesis solution separation (MHSS) architecture. Specifically, multiple incorrect-fix events are considered under each of the monitored hypotheses that assume the health status of the observations. Fault detection is performed by comparing each subset solution with the all-in-view solution. And when evaluating the protection levels, the integrity risk from the incorrectfix events is quantified under each of the monitored hypotheses. Simulation results prove the effectiveness of the proposed algorithm and show that enabling ambiguity resolution greatly benefits navigation performance.