A basin-wide significant shallow bias is found in the southern tropical Pacific thermocline in an ensemble of models from the coupled model intercomparison project phases 5 and 6. In contrast to observations, where the southern thermocline is far deeper than its northern counterpart, models have a hemispherically symmetric tropical thermocline. The shallow thermocline bias is closely related to the well known double intertropical convergence zone (ITCZ) bias, as shown by ensemble partitioning. The physical thermocline (i.e., depth of maximal vertical thermal gradient) is more strongly linked to the double ITCZ bias than the commonly used 20$^\circ$C isotherm thermocline proxy. A shallow thermocline bias is further found to be associated with wider separation of double ITCZ peaks, stronger southern precipitation, a stronger cold tongue, and a spurious south equatorial counter current. Climatic implications and feedback mechanisms between the biases are discussed.