The answer to this varies across time and space, but as a generality: reasonably common, particularly in earlier periods of colonial rule, when typical interracial relationships involved white men and African women, although there were important exceptions. In the late 19th century, stigma against such relationships increased among European communities, but they certainly did not end. Towards the end of colonial rule, relationships between African men and white women increase slightly, in part due to the number of African men studying in the UK/France. Keep in mind that these are not settler colonies, so numbers are always going to be small in proportion to the total population of a colony (there just aren't that many white people in most West African colonies). There are also interracial relationships between, for example, members of the South Asian diaspora and Africans, although this is the subject of less research; what I have seen indicates that stigma against such relationships may have been even more important within at least some parts of that diaspora (such as the Parsi community in Ghana).

For a more detailed picture, I would start with Carina Ray, Crossing the Color Line; Rachel Jean-Baptiste, Conjugal Rites (and also her two articles, “Miss Eurafrica: Men, Women’s Sexuality, and Métis Identity in Late Colonial French Africa, 1945-1960.” Journal of the History of Sexuality, Volume 20, Number 3, pp. 568-593; and “A Black Girl Should Not Be With A White Man: Sex, Race, and African Women's Social and Legal Status in Colonial Gabon, c. 1900–1946.” Journal of Women's History, Volume 22, Number 2, pp. 56-82).