This is not straightforward and a number of factors may influence the outcome. The child will complicate the separation, whether the house is owned as joint tenants or tenants-in-common, and the relative contribution each made to the entire household costs (not just the mortgage) will all have a bearing. The following is an extract from some guidance on the subject (which is not my own work):
If the couple purchased as joint tenants, either of them could apply to the court for an order that the home is to be sold and that the proceeds are to be divided equally between them.
If it's bought as tenants in common then it's assumed that both will have a beneficial interest and the property to the extent that they contributed.
If it's only owned by one of the couple, an investigation has to be made as to whether the other has an interest because they have contributed to its purchase, mortgage repayments or repair and improvement. If there has been no such contribution, what the parties said to each other or led the other to believe by their conduct may be important and what they intended has to be considered. Over the passage of time that may have altered or become blurred. It is not uncommon for one of the couple to find that, despite living together in the same home for many years owned by the other, they have no interest in the property because they made no financial contribution to it and there was no indication from the other that it was a joint property. On separation they may have to leave without any financial help from the other to re-house.
You can see that a simple "Yes/No" answer is not possible from the brief facts you have provided and a much more detailled examination of the couple's finances would have to be undertaken.