Aalberse became a member of the House of Representatives after the death of Herman Schaepman, serving from 24 February until 21 June 1916.

After the 1918 general election, Aalberse was appointed as the first Minister of Labour in the first Ruijs de Beerenbrouck cabinet, taking office on 25 September 1918.

After the 1922 general election Aalberse continued as Minister of Labour in the second Ruijs de Beerenbrouck cabinet, taking office on 18 September 1922.

After the leader of the Roman Catholic State Party and Parliamentary leader of the Roman Catholic State Party in the House of Representatives Wiel Nolens announced his retirement from national politics, Aalberse was selected as his successor, taking office on 15 September 1931.

Aalberse was elected into the municipal council of Leiden in 1899, and became alderman of Marital Status, Social Affairs and Public Hygiene of the city in 1901.

On 21 July 1898, Aalberse married Elisabeth Johanna Maria Schmier, with whom he had seven daughters and one son.