Integrity House does not specialize, per se, in treating the mentally ill. Their population is primarily the developmentally disabled (or those who used to be called "mentally retarded"). Although there are some DD clients who also have mental illness, that is a very specialized subpopulation.
McD. - One of the best agencies in O.C. specializing in permanently housing mentally ill clients is HOMES, Inc. Their program provides both the housing and the "wraparound" services required for this population. They primarily serve those that were previously homeless, but I believe that they sometimes also accept others who were not. Even if they can't help your father specifically, I would call them first to see if they can get you tied into other service providers. If you want more info, please PM me.
Bk - No, most cities, at least in SoCal, of any population (200,000 + or_) DO NOT have any services for the mentally ill, or the homeless (my particular area of expertise). While the county is working on developing a region-wide approach to addressing homelessness (and the mentally ill homeless in particular), it will take several years for the key parts of that approach to be fully operational. The county is already connected via case management software with the LA County, Long Beach, Glendale and Pasadena homeless service areas - known among service providers as a "Continuum of Care". That connection allows providers to follow the case manangement and service history of each person entered into the system (with some data blocked for privacy reasons, unless the client opts to have that data made available to other providers), with the goal of providing the most appropriate, and least duplicative service options.
As a general rule, most of the services in O.C. for these populations have revolved around Santa Ana, since most of the county agencies that serve them are there. It's also much easier to get their via public transportation, which is not true of many parts of Irvine or most of south county. And, other central and north county cities have a higher concentration of these services because (1) they are very old and well established cities, and (2) their communities have, for a variety of reasons, been less hostile to the placement of certain services and housing.