The kit distributions were carried out in Moheshkali (3500 kits), Kutubdia (1,500 kits), and Chakaria (5,115 kits) on Thursday.
Local government officials were present at the handover ceremonies in each respective sub-district.
The distributions are among a good number of programmes being taken to assist some of the poorest local host communities that have generously hosted Rohingya refugees and have been impacted by the refugee influx, said UNHCR.
Altogether 30,000 households received the family kits, which include two floor mats, a bucket, tarpaulin, rope and wire.
Other UNHCR support to Bangladeshi host communities includes programmes to assist with livelihoods, the distribution of energy-efficient LPG cooking stoves, the rehabilitation of schools, improvements to roads and drainage, as well as the installation of solar lighting.