My advice is to only use one unit or the other - but not both, for the reasons you state. Unfortunately, the TLST/EX do not have an FX loop that you can 'insert' the Boss unit into. This means that you will have to connect the units in series which is likely to degrade tone & add noise, because you can't control where he FX go in the signal chain.
I recommend you stick with the Vox Tonelab EX for quality of organic tone and because it represents very good value. It has plenty of FX in there which are likely to be all you need, plus stomp box facilities and 2 pedal sections.
If you really, really need more FX or wider FX parameter control, plus more complex connectivity/ 'outs' including FX loop, then you might want to consider a single unit that does it all. There are other solutions out there, but they all have their pros & cons. An example are the Line 6 Pod HD300/400/500 units. The HD500 has more FX and control parameters than you can poke a stick at, it has state of the art modeling, and in the HD500 you have a 2 amps at once option plus a 48s looper. It's not cheap (circa £400), and it will likely take you a long while to get your head around the unit, but at least you'll simplify your set up. It's also upgradeable via USB.
I must admit that I looked very closely at the HD500 myself - it's an impressive and great sounding bit of kit - but it takes time to find really great tone. My concern was that there was just so much in it (including complex combinations of effect chains, microphone types & positions, on top of all the amp models & FX - you can even fine tune the cabinet models!) I'd be spending my life tweaking in search of good tone, rather than playing.
The new Boss GT100 is another option, but it has similar complexity, and although it is the best sounding GT unit I've yet heard, the Boss COSM modeling still doesn't match up to the warmth and organic feel of the Tonelabs or the HD Pods. Fender has recently brought out a 'Mustang Floor' which physically is very similar to the older Vox TLSE in looks & functionality (eg 2 foot-pedals), but it lacks organic warmth & has less functionality & choice overall than the TLEX. IMHO the older Tonelab SE is actually a better unit.
The thing I love about the Vox Tonelabs is that they are very 'amp like' in functionality, very intuitive and relatively easy to use, and have a great organic tone.
As I already have a Tonelab ST, & wanted some specific features not available in the TLEX (such as FX loop, fine tune parameter controls, and patch-naming), I opted for a pre-owned Tone Lab LE which gives me everything I need, & at a quarter of the price of a HD500. Even though its no longer 'state of the art', and I don't get some of the new TLEX features/modeling, it still sounds terrific through the FX loop return of my amps, and it has some excellent features of its own.
So, its all about thinking hard about exactly what you do and don't need, & finding the right solution, at the right budget.
My 'journey' led me to the TLLE - your's may lead somewhere else...but IMHO mixing units is not the best way to go, although I'm sure there may be others here that have had success with that approach and may want to add their thoughts.