Yes, personality disorder is a mental illness. It is an inflexible, maladaptive, and rigidly pervasive pattern of behavior causing subjective distress and/or impaired functioning. The person is usually not aware of problem. Personality disorder usually presents by early adulthood.
Medically, there are three clusters of personality disorder, A, B, and C.
Cluster A personality disorder: paranoid, schizoid and schizotypal.
Cluster B personality disorder: antisocial, borderline, narcissistic and histrionic.
Cluster C personality disorder: Avoidant, obsessive compulsive and dependent.