It is no problem in QGIS to open MapInfo .tab files with combined geometry type. If a single .tab file contains points, polylines and polygons then QGIS will load three separate layers for each geometry type.
But how can I export these layers to a single .tab file after editing? It is important because many organizations (business partners) still use MapInfo and they didn't want their geospatial data structure to be modied, changed (broken).
The problem is in the symbology retaining problem. QGIS saves simple polygon and polyline symbology settings when exporting layers (but not point layers) to MapInfo .tab format. (colour of polygons and the width and colour of outline; colour and width of polylines). The edited primary .tab file doesn't contain the symbology of added objects. That's why the primary .tab file must be exported and not simply edited.
Best Answer
You can export point, line, and polygon layers into separate files and combine them with ogr2ogr.
Test data
points.mif
lines.mif
polygons.mif
ogr2ogr commands for combining points, lines, and polygons into layer "collect"
ogrinfo that confirms that all features with individual styles are now on the same layer