Little to no continuity
In March 2015, XFN (X-Files News) had interviewed with Chris Carter directly about the new miniseries, including its relationship to the Season 10 comics:
Carter also clarifies that while he thinks that IDW's The X-Files: Season 10 plot lines are very interesting, they won't be used in the revival of the TV show.
In essence, the comics were ignored during the writing of the new television series.
Also, if you read the descriptions of the plots of the issues (see here), it is fairly clear that there is essentially no continuity whatsoever between the comics and the new episodes, in the sense that primary details contradict one another. In particular, Mulder and Scully are reappointed to the X-Files under completely different circumstances and for entirely different reasons. A driving force for the mythology and the reopening of the X-Files in the comics is
a plot to kill off anyone with prior connections to the X-Files,
which is completely absent in the miniseries. In the comics, this motivates Mulder and Scully to
reopen several familiar cases from the past,
while in the miniseries, they
are assigned to exclusively fresh cases by Skinner,
at least in what we have seen so far.
Furthermore, the details of Mulder and Scully's present relationship status and Mulder's mental health in the comics are incompatible with the miniseries. In the comics, Mulder and Scully are
still in a relationship and living together,
whereas in the miniseries, Mulder and Scully
have, for some time, not been romantically involved, and Mulder is suffering from depression,
as revealed in the first episode, "My Struggle".
Given the variety of differences, it is difficult to pinpoint any continuity between the Season 10 comics and the new episodes. I would say that, on the whole, there is none.
UPDATE: Now that the first mini-series is over and we have begun yet another television miniseries, it is crystal clear that there is no overlap or continuity whatsoever between the Season 10 comics and the new television episodes.