Yes, your kids can hear your fighting
When couples visit my office I ask how their children (if they have them) respond to hearing their parents fight. No matter how many times it happens I'm still a bit stunned when parents confidently tell me their children don't know about their fights. Sometimes I hear that the children are too young to understand what's going on. Other parents think going into another room and closing the door magically eliminates the sounds of their screaming and hollering. Some couples report hollering and swearing at their partners immediately in the presence of children, but are still convinced the kids couldn't hear them because of they were watching tv or playing video games.
The truth, in fact, is much different. Even very young children are sensitive to their parent's tone of voice and volume. Infants can recognize an angry parent from a variety of non-verbal cues including facial expressions, crying sounds, hollering, and screams. Young children in particular are frequently less able to differentiate who mommy or daddy is angry with and may blame themselves for the problem. Kids may also view the fighting as a view to their personal safety or the security of the family environment. In any case the child knows that the hollering represents a risk to itself and reacts with increased stress.
Witnessing repeated inter-partner violence between parents can create PTSD in young children and increase the likelihood that they will develop internalizing or externalizing disorders later in life. Internalizing disorders include anxiety, depression, and difficulty making friends. Externalizing disorders include acting out, defiance, and juvenile delinquency. Risk of these disorders increases when the violence is repeated or experienced at a young age.
Bottom line: don't fool yourself into believing your kids don't know you're fighting with your spouse or domestic partner. Even if they don't yet have the language or courage to express it, children experience long term consequences from growing up in high conflict families. Please strongly consider seeing a marriage or family therapist to learn tools for managing and resolving conflict.
Piotrowski, C. (2011). Patterns of adjustment among siblings exposed to intimate partner violence. Journal of Family Psychology, Vol 25(1), 19-28. http://dx.doi.org/10.1037/a0022428
Tailor, K., Stewart-Tufescu, A., Piotrowski, C. (2014) Children Exposed to Intimate Partner Violence: Influences of Parenting, Family Distress, and Siblings. Journal of Family Psychology. http://dx.doi.org/10.1037/a0038584