Researchers are beginning to study how parental depression affects children. However, it must be kept in mind that mothers who are depressed also frequently have significant marital problems or other turmoil, which might better account for these research findings. For single moms, this frequently means problems related to lack of support networks, financials strains, custody battles, and controlling or abusive ex-spouses. As a result, the affects of maternal depression may, or may not be the direct cause of the problems these researchers noted. But since depression is so treatable, and because it is at least theoretically possible that your depression is having a negative affect on your children, it makes sense to seek treatment for it as soon as possible.
Some children do fine, even when their parent is having a problem.
That is, depressed parents should try to get help from professionals and not unload their problems on their children. This allows the children to continue to be children rather than caretakers. In my work, I have also found that some people try to ride out the depression, rather than seek treatment. And while it is true that, left untreated, some depressive episodes will pass, you should know that recent research suggests that leaving depression untreated worsens the prognosis for the patient. What this means is that there will be more episodes, and each untreated episode will be of worse severity than the previous one.