Deals include a 2-year fixed rate at 3.89% with a £195 arrangement and £295 completion fee and a maximum loan to value of 90%.
Adam Smith, head of mortgages at Police Mutual, said: “We are delighted to be working closely with Hinckley & Rugby Building Society who share our mutual values and our passion for service and quality.
“These are two very competitive deals with exclusivity for police officers and their families.”
Another option is a 3-year fee-free mortgage at 2.95% for purchases and remortgages up to 80% loan to value.
For both mortgages there is a free valuation for properties worth up to £1m.
Emily Smith, Hinckley & Rugby assistant business development manager, said: “We are very much looking forward to working with Police Mutual to bring the benefits of our competitive mortgages and outstanding service to its members.”