The two sides went into the game in contrasting form, with Town winless in the league in 10 games, and Solihull winning six out of their last seven.
Halifax survived a first-half barrage, including Solihull missing a penalty, to make more of a game of it after the interval, and come away with a hard-earned draw.
Town arrived at Solihull with their squad still stretched, as the seemingly weekly habit of one-player-in, one-player-out continued, with Matty Brown replacing the injured Joe Skarz; should Jamie Fullarton have wanted to change things after the defeat to Eastleigh on Saturday, he had little room to maneouvre, with again only four players on the bench.
And Solihull was probably one of the last places Town will have wanted to go, with no side having won more home games in the National League.
Sam Johnson was forced into a superb double save within the first two minutes from Jamey Osborne and Danny Wright, which set the tone for the opening half, as a combination of wasteful finishing and excellent goalkeeping kept Solihull at bay.
A nice move from left to right ended with Dayle Southwell firing off target from inside the box, but that was against the run of play, with a back-pass by Ryan Sellers being picked up by Johnson, handing the hosts a free-kick inside the box.
From Darren Carter’s driven effort, Johnson reacted well to tip over.
Harry Flowers’ rising drive was also saved by Johnson, before Danny Wright’s header was kept out too.
Jonathan Edwards latched onto a through ball to get a sight of goal at an angle, but fired well over the bar.
That was a rare Town chance though as The Shaymen struggled to maintain possession for any meaningful length of time.
Solihull looked more comfortable and composed on the ball - perhaps unsurprisingly given they came only two points off top spot - and their sharp, quick attacks proved tough to cope with for the Halifax defence.
Again the ball didn’t stick for Town when it was played upfield, meaning it was coming back at them regularly.
Southwell was Town’s best outlet on the break, producing an excellent low cross that Edwards couldn’t make contact with, and having a shot deflected behind from Matty Kosylo’s cut back.
Wright squandered a golden opportunity around the half hour mark when he blazed a penalty over the bar after Jermaine Hylton had raced clear, and dribbled round Johnson before being fouled by Matty Brown.
Hylton then thought he had scored soon afterwards but his header was deemed not to have crossed the line.
From another left-wing cross, Wright headed over before Adi Yussuf’s low shot was saved after some fantastic skill by Hylton to get past Jacob Hanson.
Darren Carter squeezed one more effort in before half-time after a flowing move when Town were caught in possession, but Johnson saved his shot.
Town had made it through the first 45 minutes unscathed, and seemed to have stopped the flow of Solihull chances to barely a trickle after the interval.
Town offered a sporadic threat on the break, getting into some decent positions but lacking the cutting edge to find the final pass or shot.
Solihull were having to be more patient now, finding their route to goal much harder to navigate.
Cameron King saw a shot blocked after bursting into the box with 15 minutes remaining, as Town perhaps sensed they could grab all three points.
Hanson’s cross from the right was missed by two team-mates in the box as Halifax now looked the more threatening as the game wore on.
Yussuf was off target in the final 10 minutes, before Southwell charged towards goal at an angle but failed to get a shot at goal.
Solihull: Boot, Williams, Daly, Flowers, Reckford, Osborne, Carter, Storer (Maxwell 85), Hylton (Stenson 69), Yussuf, Wright (Thomas 71). Subs not used: Carline, O’Keefe.
Shots on target: 8
Shots off target: 10
Halifax: Johnson, Hanson, Clarke, Brown, Sellers, Maher, Staunton, King, Southwell, Kosylo, Edwards. Subs not used: Rowley, Lenighan, McLeod, Odelusi.
Shots on target: 2
Shots off target: 5
Referee: Josh Smith
Town man of the match: Sam Johnson