For a simple line and point you can just use IFeatureEdit2.SplitWithUpdate to split the line and update the attributes.IFeatureEdit2 featureEdit = lineFeature as IFeatureEdit2;
featureEdit.SplitWithUpdate(splitPoint);
Alternatively you can keep the returned ISet to do something useful, like keep all the lines selected in this example. IFeatureEdit2 featureEdit = lineFeature as IFeatureEdit2;
//select features after split
featSelection.Add(lineFeature);
ISet newSet = featureEdit.SplitWithUpdate(splitPoint);
newSet.Reset();
IFeature newFeat = newSet.Next() as IFeature;
featSelection.Add(newFeat);