Hydrophilic polymers have garnered much attention due to their critical roles in various applications such as molecular separation membranes, bio-interfaces, and surface engineering. However, a long-standing problem is that their mechanical properties usually deteriorate at high relative humidity (RH). Through the simultaneous incorporation of functionalized carbon nanotubes and copper ions (Cu(2+)), this study introduces a facile method to fabricate high strength polyelectrolyte complex nanohybrid membranes resistant to high RH (90%). For example, the tensile strength of the nanohybrid membranes is 55 MPa at 90% RH (80% of the original value at 30% RH). These results are explained by copper ions depressing the swelling degree of the membrane, and functionalized carbon nanotubes promoting stress transfer between the polymer matrix and them. The nanohybrid membranes are efficient in separating water/alcohol mixtures containing relatively high water content (up to 30 wt%), whereas common hydrophilic polymer membranes usually suffer from excessive swelling under this condition.