Stephen Wicks was arrested in Longley Road on the evening of Monday 12 October 2020, following a report a woman had been assaulted at a nearby private address.
While being detained, the 27-year-old, of Luton Road, Chatham, is then alleged to have thrown several punches at two attending officers.
All three victims sustained facial injuries.
Mr Wicks has been charged with one count of assault by beating, for the assault on the woman, and two counts of actual bodily harm, for the assaults on the police constables.
He appeared at Medway Magistrates’ Court on Wednesday 14 October and has been remanded in custody to appear at Maidstone Crown Court on Wednesday 11 November.