Praise be to Allaah.
Yes, it is permissible for him to be present when she is giving birth, because it is permissible for the husband to see all of his wife’s body with no exceptions. Anas ibn Maalik (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) and one of his wives used to do ghusl from janaabah from one vessel. (Narrated by al-Bukhaari, 264).
So there is nothing wrong with a man attending when his wife gives birth, so long as other women are not uncovered in the same place. And Allaah knows best.
Sheikh Muhammed Salih Al-Munajjid