Background: A range of endophenotypes characterise psychosis, however there has been limited work understanding if and how they are inter-related. Methods: This multi-centre study includes 8754 participants: 2212 people with a psychotic disorder, 1487 unaffected relatives of probands, and 5055 healthy controls. We investigated cognition [digit span (N = 3127), block design (N = 5491), and the Rey Auditory Verbal Learning Test (N = 3543)], electrophysiology [P300 amplitude and latency (N = 1102)], and neuroanatomy [lateral ventricular volume (N = 1721)]. We used linear regression to assess the interrelationships between endophenotypes. Results: The P300 amplitude and latency were not associated (regression coef. −0.06, 95% CI −0.12 to 0.01, p = 0.060), and P300 amplitude was positively associated with block design (coef. 0.19, 95% CI 0.10–0.28, p < 0.001). There was no evidence of associations between lateral ventricular volume and the other measures (all p > 0.38). All the cognitive endophenotypes were associated with each other in the expected directions (all p < 0.001). Lastly, the relationships between pairs of endophenotypes were consistent in all three participant groups, differing for some of the cognitive pairings only in the strengths of the relationships. Conclusions: The P300 amplitude and latency are independent endophenotypes; the former indexing spatial visualisation and working memory, and the latter is hypothesised to index basic processing speed. Individuals with psychotic illnesses, their unaffected relatives, and healthy controls all show similar patterns of associations between endophenotypes, endorsing the theory of a continuum of psychosis liability across the population.