Campbell -- who joined Leppard in 1992 -- filed docs in Los Angeles County Superior Court ... citing irreconcilable differences.
According to docs ... the rock-star couple tied the knot waaaaay back in Feb. 1987. They have two young daughters together, ages 13 and 11.
Campbell is asking for joint legal and physical custody of the girls ... he's asking the judge to deny spousal support to Julie.
We reached out to Vivian for comment ... so far no word back.