Many brain diseases and disorders lack objective measures of brain function as indicators of pathology. The search for brain function biomarkers is complicated by the fact that these conditions are often heterogeneous and described as a spectrum from normal to abnormal rather than a sick-healthy dichotomy. Normative modeling addresses these challenges by characterizing the normal variation of brain function given sex and age and identifying abnormalities as deviations from this norm. Focusing on functional connectivity (FC) as a way to capture the network properties of the brain's activity, we here argue that the pathological effects of neurological or psychiatric disease lie at the systemic level, and that whole-brain normative models are more suitable to capture individual variations associated to these complex conditions than existing localized approaches that analyze one connection at a time. To be able to capture the whole-brain effects of disease, we thus propose Functional Connectivity Integrative Normative Modeling (FUNCOIN) as a novel whole-brain approach to normative modeling of FC. Using FUNCOIN and UK Biobank resting-state fMRI data from 46,000 healthy subjects across training and testing sets, we found that subjects with bipolar disorder and Parkinson's disease were significantly, and substantially, more likely than healthy subjects to exhibit abnormal FC patterns, which was not seen in localized models. Subjects with bipolar disorder divided into two distinct subgroups characterized by different brain function deviations. In Parkinson's disease subjects, abnormal FC patterns were significant even on scans up to 8 years before diagnosis.