The brief answer is “yes”. Both parents have the joint responsibility of covering the children’s expenses.
Several relevant factors would have to be considered in getting each parent to contribute towards such expenses, eg what is the station in life of the children, what is the total amount of the children’s expenses and what is the affordability of each parent in contributing towards such expenses.
Even if the wife’s income is sufficiently high to cover all the children’s expenses, the husband is usually required to contribute towards such expenses, since the responsibility is joint. The more affluent parent may have to contribute a larger share of such expenses.
Would I have to share my assets with my spouse?
The answer is “yes” insofar as matrimonial assets are concerned. In essence, matrimonial assets are those assets which are acquired by the parties during the marriage and those assets which are acquired pre-marriage by a party but improvements have been made to those assets by the spouse during the marriage.
The proportion to be shared depends on both direct and indirect contributions. Direct contributions inevitably refer to financial contributions towards the acquisition of the asset.
Indirect contributions are more general in nature, such as time and effort expended in minding the children and running the household which relieved the other spouse from such work and provided the opportunity of earning money.