Is it permissible to tell ones family of a pregnancy before three months?

Firstly:

We ask Allaah to bless you with righteous offspring and to bless this child. 

Secondly: 

There is nothing wrong with telling other people about the pregnancy after you find out about it, and it is not essential to wait until three months have passed. Rather it is permissible to tell others before then, but you should limit that to family and close friends only.

This is a general principle which should be paid attention to when telling others of blessings. The news should be given only to those who wish good for you and will rejoice over it, so as to ward off the evil eye and destructive envy (hasad). 

The evidence for that is the words of the Prophet (peace and blessings of Allaah be upon him): “Be discreet in order to achieve what you want, for everyone who is blessed is envied.” Narrated by al-Tabaraani and Abu Nu’aym; classed as sahaah by al-Albaani in Saheeh al-Jaami’, no. 943. 

And Allaah knows best.