public string SpatialRelationshipDescription {get; set;}

public void FindSpatiallyRelatedFeaturesUsingDE9IMPredicate(Geodatabase geodatabase, FeatureClass polygonFeatureClass, FeatureClass polylineFeatureClass)
{
    using (RowCursor polygonRowCursor = polygonFeatureClass.Search(new QueryFilter()))
    {
        if (polygonRowCursor.MoveNext())
        {
            using (Feature polygonFeature = polygonRowCursor.Current as Feature)
            {
                // DE9IM predicate string to find overlapping features
                string overlappingDE9IM = "1*T***T**";

                SpatialQueryFilter spatialQueryFilter = new SpatialQueryFilter()
                {
                    FilterGeometry = polygonFeature.GetShape(),
                    SpatialRelationship = SpatialRelationship.Relation,
                    SpatialRelationshipDescription = overlappingDE9IM
                };

                using (RowCursor overlappingPolyline = polylineFeatureClass.Search(spatialQueryFilter))
                {
                    while (overlappingPolyline.MoveNext())
                    {
                        // Overlapping polylines on the polygon
                    }
                }
            }
        }
    }
}