At my company, female employees with young children never get promoted. Although the company doesn't seem to treat men better than women generally, mothers really get left behind. When I applied for a management position, my supervisor asked me whether I was willing to put in the longer hours the position requires, given that I have kids at home. He also questioned whether I'd "really" be willing to travel when the time came to attend company meetings in other cities, and talked about how difficult his wife found it to leave their kids overnight. I've never given my employer any reason to think I wouldn't do my job. All of my performance evaluations are stellar, and I'm ready for more responsiblity. Not that it's any business of my company's, but my husband handles most of the child care in our family. Isn't this sex discrimination?
What you are describing is often called "sex plus" discrimination. It's illegal only if the employer is making decisions based on gender, not on the "plus." Here's what I mean:
It's not illegal to discriminate based on parental status alone. Title VII and the other federal laws that ban employment discrimination apply only to certain traits, called "protected characteristics." They include race, color, national origin, sex, religion, disability, age, and genetic information. But they don't prohibit discrimination based on parenthood. So, if your employer was treating fathers and mothers equally badly, that would be legal. Perhaps neither smart nor ethical, but legal. The plus, in your case, is being a parent of young children. If that fact alone is driving the employer's decisions, it is not illegal discrimination.
However, if your company treats male employees with young children differently than female employees with young children, the plus is taken out of the equation. In this situation, the employer's decisions are really based on the gender of the parent, not the fact of parenthood. Your supervisor's questions reveal that this might be the case. After all, we still have very gendered notions about child care and work outside the home. If your employer's decisions are based on sexist opinions that women should stay home or curtail their careers after having children, or on outdated assumptions that mothers will be unwilling to put in long hours, leave their kids overnight, or give their full focus to their jobs, that is sex discrimination.
You don't mention how the fathers at your company are treated. But if they still have opportunities for promotion after having kids, there may be a sex plus claim here.