The pair agreed to temporary charge after Phillips and Halford guide the Robins for the last time in The Emirates FA Cup on Saturday when they host Nantwich Town at Hurst Cross before taking control of Stalybridge Celtic.
Appointed three years ago as the successors to Craig Robinson, they insisted on staying on for the tie after agreeing to replace former Southport boss Liam Watson at Bower Fold.
The Robins say they are in no hurry to rush into an appointment after naming the experienced Banim and Haining but have set a deadline of Monday 12 September for potential candidates to express their interest and send their footballing CVs to chairman Terry Hollis.
In a statement announcing their appointments, the club also the left the door open for the caretaking duo to join the shortlist of prospective candidates they'll be drawing up to interview.
The Robins said: "Ashton United have moved to appoint senior players Will Haining and Jody Banim as caretaker managers until such time as the club can consider a more permanent appointment.
"Both men have vast knowledge and experience of the game and the club is confident that they can 'hold the fort' until such time as a permanent successor is found, if indeed that is needed following their tenure.
"The club is in no rush to make an appointment following the departure of Paul Phillips and Steve Halford to Stalybridge Celtic and will be pleased to receive applications for the vacant post from interested parties."
Prolific scorer Banim, 38, was at Radcliffe Borough last season after a career that has taken in Manchester United, Trafford, Altrincham, Flixton, Hyde United, Rossendale United, Radcliffe Borough, Shrewsbury Town and Accrington Stanley.
Haining, pictured above, played nearly 200 games for Oldham Athletic. The 33-year-old has also turned out for Falkirk, Glasgow Rangers, St Mirren, Morecambe, Fleetwood Town, Hyde and Macclesfield Town.
To apply for the post email: terryhollis@rol-lite.co.uk.
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