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.
A personality disorder can be considered to be a mental illness simply because it affects the way that the person interacts with others. It will affect how people would cope with their lives. Some people who have mental disorders are unable to go to work or even do their tasks well. Take note that there are different types of personality disorders.
Some are so subtle that people may not even realize that they have it. People who have personality disorders are recommended to talk to their therapists about the things that they are going through. Some people are able to recover through therapy and the support of their family members and friends.