Temple University radio, WRTI, is classical by day and jazz by night. On their HD-2 channel they reverse the formats and do jazz by day and classical by night. They used to be all jazz but when another public radio station flipped to news and information and a commercial classical station also flipped, they adopted this split schedule (in typical public sector fashion - trying to compromise by pleasing nobody).
This isn't day and night but NJ 101.5 does talk weekdays and classic hits on weekends. A smart move. Talk usually bombs on weekends and stations end up doing "best of" segments or running infomercials (often disguised as how-to talk shows). NJ 101.5 oldies playlist targets the same age group their talk shows reach. Oldies start Friday evening and run through Sunday overnight.
Many smaller market public radio stations still run the "tent pole" format: NPR news magazines in morning and afternoon drive plus maybe Fresh Air or something in there someplace. Typically, they run classical middays and jazz at night. Even some folk on the weekends. A lot of public radio stations in larger markets used to do this, too, but now almost all have opted for a consistent format. One notable exception is KCRW, Santa Monica (LA market).
This used to be block programming and it was the norm before wall-to-wall formats. Even AM top 40 stations or popular music stations used to vary their playlists considerable between daytime and evening hours. During the day, when kids were in school, playlists were softer hits and even some MOR. At night, for the teen audience while parental units watched TV, they skewed toward hard rock.