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
          }
        }
      }
    }
  }
}